Av(1234, 2431)
View Raw Data
Generating Function
11x965x8+195x7365x6+447x5359x4+189x363x2+12x1(x23x+1)(2x1)2(1+x)6
Counting Sequence
1, 1, 2, 6, 22, 86, 330, 1198, 4087, 13185, 40619, 120636, 348197, 983073, 2728722, ...
Implicit Equation for the Generating Function
(x23x+1)(2x1)2(1+x)6F(x)+11x965x8+195x7365x6+447x5359x4+189x363x2+12x1=0
Recurrence
a(0)=1
a(1)=1
a(2)=2
a(3)=6
a(4)=22
a(5)=86
a(6)=330
a(7)=1198
a(8)=4087
a(9)=13185
a(n+4)=n5120n4245n324+73n2244a(n)+16a(n+1)17a(n+2)+7a(n+3)+73n60+2,n10
Explicit Closed Form
(125+540)(3252)n120+(125+540)(32+52)n120+n5120+n412+23n324+23n212321+nn+391n30182n+10
Heatmap

To create this heatmap, we sampled 1,000,000 permutations of length 300 uniformly at random. The color of the point (i,j) represents how many permutations have value j at index i (darker = more).

This specification was found using the strategy pack "Point Placements" and has 268 rules.

Found on January 18, 2022.

Finding the specification took 29 seconds.

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Copy 268 equations to clipboard:
F0(x)=F1(x)+F2(x)F1(x)=1F2(x)=F3(x)F3(x)=F4(x)F5(x)F4(x)=xF5(x)=F37(x)+F6(x)F6(x)=F1(x)+F7(x)F7(x)=F8(x)F8(x)=F4(x)F9(x)F9(x)=F10(x)+F13(x)F10(x)=F1(x)+F11(x)F11(x)=F12(x)F12(x)=F10(x)F4(x)F13(x)=F14(x)+F7(x)F14(x)=F15(x)+F16(x)+F35(x)F15(x)=0F16(x)=F17(x)F4(x)F17(x)=F18(x)+F22(x)F18(x)=F11(x)+F19(x)F19(x)=F20(x)F20(x)=F21(x)F4(x)F21(x)=F11(x)F22(x)=F14(x)+F23(x)F23(x)=2F15(x)+F24(x)+F28(x)F24(x)=F25(x)F4(x)F25(x)=F26(x)+F27(x)F26(x)=F19(x)F27(x)=F23(x)F28(x)=F29(x)F4(x)F29(x)=F30(x)F30(x)=F31(x)F31(x)=F32(x)F4(x)F32(x)=F33(x)+F34(x)F33(x)=F11(x)F34(x)=F30(x)F35(x)=F36(x)F4(x)F36(x)=F30(x)+F7(x)F37(x)=F2(x)+F38(x)F38(x)=F15(x)+F265(x)+F39(x)F39(x)=F4(x)F40(x)F40(x)=F41(x)+F55(x)F41(x)=F42(x)+F7(x)F42(x)=F15(x)+F16(x)+F43(x)F43(x)=F4(x)F44(x)F44(x)=F13(x)+F45(x)F45(x)=F46(x)+F47(x)F46(x)=F31(x)F47(x)=2F15(x)+F48(x)+F53(x)F48(x)=F4(x)F49(x)F49(x)=F50(x)+F51(x)F50(x)=F19(x)F51(x)=F52(x)F52(x)=2F15(x)+F28(x)+F48(x)F53(x)=F4(x)F54(x)F54(x)=F46(x)F55(x)=F38(x)+F56(x)F56(x)=F15(x)+F234(x)+F262(x)+F57(x)F57(x)=F4(x)F58(x)F58(x)=F59(x)+F66(x)F59(x)=F42(x)+F60(x)F60(x)=F15(x)+F24(x)+F61(x)+F64(x)F61(x)=F4(x)F62(x)F62(x)=F22(x)+F63(x)F63(x)=F47(x)F64(x)=F4(x)F65(x)F65(x)=F45(x)F66(x)=F56(x)+F67(x)F67(x)=F116(x)+F15(x)+F163(x)+F231(x)+F68(x)F68(x)=F4(x)F69(x)F69(x)=F70(x)+F78(x)F70(x)=F60(x)+F71(x)F71(x)=F15(x)+F72(x)+F73(x)+F75(x)+F77(x)F72(x)=0F73(x)=F4(x)F74(x)F74(x)=F27(x)F75(x)=F4(x)F76(x)F76(x)=F63(x)F77(x)=0F78(x)=F67(x)+F79(x)F79(x)=F100(x)+F115(x)+F15(x)+F80(x)+F84(x)+F85(x)F80(x)=F4(x)F81(x)F81(x)=F82(x)+F83(x)F82(x)=F71(x)F83(x)=F79(x)F84(x)=0F85(x)=F4(x)F86(x)F86(x)=F87(x)F87(x)=F88(x)F88(x)=3F15(x)+F89(x)+F93(x)F89(x)=F4(x)F90(x)F90(x)=F91(x)+F92(x)F91(x)=F23(x)F92(x)=F88(x)F93(x)=F4(x)F94(x)F94(x)=F95(x)F95(x)=F96(x)F96(x)=F4(x)F97(x)F97(x)=F98(x)+F99(x)F98(x)=F30(x)F99(x)=F95(x)F100(x)=F101(x)F4(x)F101(x)=F102(x)F102(x)=F103(x)F103(x)=3F15(x)+F104(x)+F108(x)F104(x)=F105(x)F4(x)F105(x)=F106(x)+F107(x)F106(x)=F47(x)F107(x)=F103(x)F108(x)=F109(x)F4(x)F109(x)=F110(x)F110(x)=F111(x)F111(x)=F112(x)F4(x)F112(x)=F113(x)+F114(x)F113(x)=F46(x)F114(x)=F110(x)F115(x)=0F116(x)=F117(x)F4(x)F117(x)=F118(x)+F87(x)F118(x)=F119(x)F119(x)=2F15(x)+F120(x)+F136(x)F120(x)=F121(x)F4(x)F121(x)=F122(x)+F123(x)F122(x)=F19(x)+F23(x)F123(x)=F119(x)+F124(x)F124(x)=2F15(x)+F116(x)+F125(x)+F93(x)F125(x)=F126(x)F4(x)F126(x)=F127(x)+F129(x)F127(x)=F128(x)+F23(x)F128(x)=F73(x)F129(x)=F124(x)+F130(x)F130(x)=2F15(x)+F131(x)+F135(x)+F84(x)+F85(x)F131(x)=F132(x)F4(x)F132(x)=F133(x)+F134(x)F133(x)=F128(x)F134(x)=F130(x)F135(x)=0F136(x)=F137(x)F4(x)F137(x)=F138(x)F138(x)=F139(x)F139(x)=F140(x)F4(x)F140(x)=F141(x)+F142(x)F141(x)=F11(x)+F30(x)F142(x)=F138(x)+F143(x)F143(x)=2F15(x)+F144(x)+F160(x)F144(x)=F145(x)F4(x)F145(x)=F146(x)+F150(x)F146(x)=F147(x)+F30(x)F147(x)=F148(x)F148(x)=F149(x)F4(x)F149(x)=F34(x)F150(x)=F143(x)+F151(x)F151(x)=2F15(x)+F152(x)+F156(x)+F157(x)F152(x)=F153(x)F4(x)F153(x)=F154(x)+F155(x)F154(x)=F147(x)F155(x)=F151(x)F156(x)=0F157(x)=F158(x)F4(x)F158(x)=F159(x)F159(x)=F95(x)F160(x)=F161(x)F4(x)F161(x)=F159(x)+F162(x)F162(x)=F138(x)F163(x)=F164(x)F4(x)F164(x)=F102(x)+F165(x)F165(x)=F166(x)+F88(x)F166(x)=2F15(x)+F167(x)+F213(x)F167(x)=F168(x)F4(x)F168(x)=F169(x)+F170(x)F169(x)=F14(x)+F47(x)F170(x)=F166(x)+F171(x)F171(x)=2F15(x)+F108(x)+F172(x)+F194(x)F172(x)=F173(x)F4(x)F173(x)=F174(x)+F178(x)F174(x)=F175(x)+F47(x)F175(x)=F176(x)F176(x)=F177(x)F4(x)F177(x)=F51(x)F178(x)=F171(x)+F179(x)F179(x)=2F15(x)+F180(x)+F184(x)+F185(x)+F193(x)F180(x)=F181(x)F4(x)F181(x)=F182(x)+F183(x)F182(x)=F175(x)F183(x)=F179(x)F184(x)=0F185(x)=F186(x)F4(x)F186(x)=F187(x)F187(x)=F188(x)F188(x)=3F15(x)+F189(x)+F93(x)F189(x)=F190(x)F4(x)F190(x)=F191(x)+F192(x)F191(x)=F52(x)F192(x)=F188(x)F193(x)=0F194(x)=F195(x)F4(x)F195(x)=F187(x)+F196(x)F196(x)=F197(x)F197(x)=2F15(x)+F136(x)+F198(x)F198(x)=F199(x)F4(x)F199(x)=F200(x)+F201(x)F200(x)=F19(x)+F52(x)F201(x)=F197(x)+F202(x)F202(x)=2F15(x)+F194(x)+F203(x)+F93(x)F203(x)=F204(x)F4(x)F204(x)=F205(x)+F207(x)F205(x)=F206(x)+F52(x)F206(x)=F176(x)F207(x)=F202(x)+F208(x)F208(x)=2F15(x)+F135(x)+F184(x)+F185(x)+F209(x)F209(x)=F210(x)F4(x)F210(x)=F211(x)+F212(x)F211(x)=F206(x)F212(x)=F208(x)F213(x)=F214(x)F4(x)F214(x)=F215(x)+F95(x)F215(x)=F216(x)F216(x)=F217(x)F4(x)F217(x)=F218(x)+F219(x)F218(x)=F46(x)+F7(x)F219(x)=F215(x)+F220(x)F220(x)=2F15(x)+F160(x)+F221(x)F221(x)=F222(x)F4(x)F222(x)=F223(x)+F225(x)F223(x)=F224(x)+F46(x)F224(x)=F148(x)F225(x)=F220(x)+F226(x)F226(x)=2F15(x)+F156(x)+F157(x)+F227(x)F227(x)=F228(x)F4(x)F228(x)=F229(x)+F230(x)F229(x)=F224(x)F230(x)=F226(x)F231(x)=F232(x)F4(x)F232(x)=F233(x)F233(x)=F103(x)+F110(x)F234(x)=F235(x)F4(x)F235(x)=F165(x)+F236(x)F236(x)=F119(x)+F237(x)F237(x)=F15(x)+F238(x)+F260(x)F238(x)=F239(x)F4(x)F239(x)=F240(x)+F241(x)F240(x)=F11(x)+F14(x)F241(x)=F237(x)+F242(x)F242(x)=F15(x)+F213(x)+F234(x)+F243(x)F243(x)=F244(x)F4(x)F244(x)=F245(x)+F247(x)F245(x)=F14(x)+F246(x)F246(x)=F15(x)+F24(x)+F53(x)+F61(x)F247(x)=F242(x)+F248(x)F248(x)=F108(x)+F116(x)+F15(x)+F163(x)+F249(x)F249(x)=F250(x)F4(x)F250(x)=F251(x)+F254(x)F251(x)=F246(x)+F252(x)F252(x)=F15(x)+F253(x)+F72(x)+F73(x)+F75(x)F253(x)=0F254(x)=F248(x)+F255(x)F255(x)=F100(x)+F15(x)+F193(x)+F256(x)+F84(x)+F85(x)F256(x)=F257(x)F4(x)F257(x)=F258(x)+F259(x)F258(x)=F252(x)F259(x)=F255(x)F260(x)=F261(x)F4(x)F261(x)=F138(x)+F2(x)F262(x)=F263(x)F4(x)F263(x)=F233(x)+F264(x)F264(x)=F166(x)+F215(x)F265(x)=F266(x)F4(x)F266(x)=F264(x)+F267(x)F267(x)=F2(x)+F237(x)

This specification was found using the strategy pack "Regular Insertion Encoding Bottom" and has 393 rules.

Found on April 28, 2021.

Finding the specification took 13 seconds.

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F0(x)=F1(x)+F2(x)F1(x)=1F2(x)=F3(x)F3(x)=F13(x)F4(x)F4(x)=F0(x)+F5(x)F5(x)=F36(x)+F6(x)F6(x)=F7(x)F7(x)=F13(x)F8(x)F8(x)=F10(x)+F9(x)F9(x)=F1(x)+F6(x)F10(x)=F11(x)+F15(x)F11(x)=F12(x)F12(x)=F13(x)F14(x)F13(x)=xF14(x)=F1(x)+F11(x)F15(x)=F16(x)+F17(x)+F19(x)F16(x)=0F17(x)=F13(x)F18(x)F18(x)=F15(x)+F6(x)F19(x)=F13(x)F20(x)F20(x)=F21(x)+F25(x)F21(x)=F11(x)+F22(x)F22(x)=F23(x)F23(x)=F13(x)F24(x)F24(x)=F21(x)F25(x)=F26(x)+F29(x)F26(x)=F27(x)F27(x)=F13(x)F28(x)F28(x)=F11(x)+F26(x)F29(x)=F30(x)F30(x)=F13(x)F31(x)F31(x)=F32(x)F32(x)=F26(x)+F33(x)F33(x)=F34(x)F34(x)=F13(x)F35(x)F35(x)=F32(x)F36(x)=F16(x)+F325(x)+F37(x)F37(x)=F13(x)F38(x)F38(x)=F39(x)+F40(x)F39(x)=F2(x)+F36(x)F40(x)=F186(x)+F41(x)F41(x)=F16(x)+F42(x)+F44(x)F42(x)=F13(x)F43(x)F43(x)=F2(x)+F41(x)F44(x)=F13(x)F45(x)F45(x)=F46(x)+F73(x)F46(x)=F11(x)+F47(x)F47(x)=F48(x)F48(x)=F13(x)F49(x)F49(x)=F46(x)+F50(x)F50(x)=F22(x)+F51(x)F51(x)=2F16(x)+F52(x)+F55(x)F52(x)=F13(x)F53(x)F53(x)=F54(x)F54(x)=F47(x)+F51(x)F55(x)=F13(x)F56(x)F56(x)=F57(x)+F61(x)F57(x)=F22(x)+F58(x)F58(x)=F59(x)F59(x)=F13(x)F60(x)F60(x)=F57(x)F61(x)=F62(x)+F66(x)F62(x)=F63(x)F63(x)=F13(x)F64(x)F64(x)=F65(x)F65(x)=F22(x)+F62(x)F66(x)=F67(x)F67(x)=F13(x)F68(x)F68(x)=F69(x)F69(x)=F62(x)+F70(x)F70(x)=F71(x)F71(x)=F13(x)F72(x)F72(x)=F69(x)F73(x)=F15(x)+F74(x)F74(x)=2F16(x)+F141(x)+F75(x)F75(x)=F13(x)F76(x)F76(x)=F54(x)+F77(x)F77(x)=F129(x)+F78(x)F78(x)=F79(x)F79(x)=F13(x)F80(x)F80(x)=F108(x)+F81(x)F81(x)=F26(x)+F82(x)F82(x)=F83(x)F83(x)=F13(x)F84(x)F84(x)=F81(x)+F85(x)F85(x)=F33(x)+F86(x)F86(x)=3F16(x)+F87(x)+F90(x)F87(x)=F13(x)F88(x)F88(x)=F89(x)F89(x)=F82(x)+F86(x)F90(x)=F13(x)F91(x)F91(x)=F92(x)+F96(x)F92(x)=F33(x)+F93(x)F93(x)=F94(x)F94(x)=F13(x)F95(x)F95(x)=F92(x)F96(x)=F101(x)+F97(x)F97(x)=F98(x)F98(x)=F13(x)F99(x)F99(x)=F100(x)F100(x)=F33(x)+F97(x)F101(x)=F102(x)F102(x)=F103(x)F13(x)F103(x)=F104(x)F104(x)=F105(x)+F97(x)F105(x)=F106(x)F106(x)=F107(x)F13(x)F107(x)=F104(x)F108(x)=F109(x)+F29(x)F109(x)=3F16(x)+F110(x)+F112(x)F110(x)=F111(x)F13(x)F111(x)=F89(x)F112(x)=F113(x)F13(x)F113(x)=F114(x)+F118(x)F114(x)=F115(x)+F29(x)F115(x)=F116(x)F116(x)=F117(x)F13(x)F117(x)=F114(x)F118(x)=F119(x)+F122(x)F119(x)=F120(x)F120(x)=F121(x)F13(x)F121(x)=F100(x)F122(x)=F123(x)F123(x)=F124(x)F13(x)F124(x)=F125(x)F125(x)=F119(x)+F126(x)F126(x)=F127(x)F127(x)=F128(x)F13(x)F128(x)=F125(x)F129(x)=3F16(x)+F110(x)+F130(x)F130(x)=F13(x)F131(x)F131(x)=F114(x)+F132(x)F132(x)=F133(x)+F134(x)F133(x)=F120(x)F134(x)=F135(x)F135(x)=F13(x)F136(x)F136(x)=F137(x)F137(x)=F133(x)+F138(x)F138(x)=F139(x)F139(x)=F13(x)F140(x)F140(x)=F137(x)F141(x)=F13(x)F142(x)F142(x)=F143(x)+F165(x)F143(x)=F144(x)+F15(x)F144(x)=F145(x)F145(x)=F13(x)F146(x)F146(x)=F143(x)+F147(x)F147(x)=F148(x)+F149(x)F148(x)=F34(x)F149(x)=3F16(x)+F150(x)+F87(x)F150(x)=F13(x)F151(x)F151(x)=F152(x)+F156(x)F152(x)=F148(x)+F153(x)F153(x)=F154(x)F154(x)=F13(x)F155(x)F155(x)=F152(x)F156(x)=F157(x)+F158(x)F157(x)=F98(x)F158(x)=F159(x)F159(x)=F13(x)F160(x)F160(x)=F161(x)F161(x)=F157(x)+F162(x)F162(x)=F163(x)F163(x)=F13(x)F164(x)F164(x)=F161(x)F165(x)=F166(x)+F170(x)F166(x)=2F16(x)+F167(x)+F30(x)F167(x)=F13(x)F168(x)F168(x)=F169(x)+F65(x)F169(x)=F133(x)+F29(x)F170(x)=3F16(x)+F110(x)+F171(x)F171(x)=F13(x)F172(x)F172(x)=F173(x)+F177(x)F173(x)=F166(x)+F174(x)F174(x)=F175(x)F175(x)=F13(x)F176(x)F176(x)=F173(x)F177(x)=F178(x)+F179(x)F178(x)=F120(x)F179(x)=F180(x)F180(x)=F13(x)F181(x)F181(x)=F182(x)F182(x)=F178(x)+F183(x)F183(x)=F184(x)F184(x)=F13(x)F185(x)F185(x)=F182(x)F186(x)=F16(x)+F187(x)+F189(x)+F75(x)F187(x)=F13(x)F188(x)F188(x)=F186(x)+F36(x)F189(x)=F13(x)F190(x)F190(x)=F143(x)+F191(x)F191(x)=F192(x)+F213(x)F192(x)=F16(x)+F167(x)+F193(x)+F200(x)F193(x)=F13(x)F194(x)F194(x)=F192(x)+F195(x)F195(x)=F16(x)+F19(x)+F196(x)F196(x)=F13(x)F197(x)F197(x)=F198(x)+F199(x)F198(x)=F195(x)+F6(x)F199(x)=F15(x)+F192(x)F200(x)=F13(x)F201(x)F201(x)=F202(x)+F32(x)F202(x)=F203(x)+F206(x)F203(x)=F204(x)F204(x)=F13(x)F205(x)F205(x)=F203(x)+F26(x)F206(x)=F207(x)F207(x)=F13(x)F208(x)F208(x)=F209(x)F209(x)=F203(x)+F210(x)F210(x)=F211(x)F211(x)=F13(x)F212(x)F212(x)=F209(x)F213(x)=3F16(x)+F214(x)+F280(x)F214(x)=F13(x)F215(x)F215(x)=F216(x)+F89(x)F216(x)=F217(x)+F268(x)F217(x)=F218(x)F218(x)=F13(x)F219(x)F219(x)=F220(x)+F247(x)F220(x)=F203(x)+F221(x)F221(x)=F222(x)F222(x)=F13(x)F223(x)F223(x)=F220(x)+F224(x)F224(x)=F210(x)+F225(x)F225(x)=4F16(x)+F226(x)+F229(x)F226(x)=F13(x)F227(x)F227(x)=F228(x)F228(x)=F221(x)+F225(x)F229(x)=F13(x)F230(x)F230(x)=F231(x)+F235(x)F231(x)=F210(x)+F232(x)F232(x)=F233(x)F233(x)=F13(x)F234(x)F234(x)=F231(x)F235(x)=F236(x)+F240(x)F236(x)=F237(x)F237(x)=F13(x)F238(x)F238(x)=F239(x)F239(x)=F210(x)+F236(x)F240(x)=F241(x)F241(x)=F13(x)F242(x)F242(x)=F243(x)F243(x)=F236(x)+F244(x)F244(x)=F245(x)F245(x)=F13(x)F246(x)F246(x)=F243(x)F247(x)=F206(x)+F248(x)F248(x)=4F16(x)+F249(x)+F251(x)F249(x)=F13(x)F250(x)F250(x)=F228(x)F251(x)=F13(x)F252(x)F252(x)=F253(x)+F257(x)F253(x)=F206(x)+F254(x)F254(x)=F255(x)F255(x)=F13(x)F256(x)F256(x)=F253(x)F257(x)=F258(x)+F261(x)F258(x)=F259(x)F259(x)=F13(x)F260(x)F260(x)=F239(x)F261(x)=F262(x)F262(x)=F13(x)F263(x)F263(x)=F264(x)F264(x)=F258(x)+F265(x)F265(x)=F266(x)F266(x)=F13(x)F267(x)F267(x)=F264(x)F268(x)=4F16(x)+F249(x)+F269(x)F269(x)=F13(x)F270(x)F270(x)=F253(x)+F271(x)F271(x)=F272(x)+F273(x)F272(x)=F259(x)F273(x)=F274(x)F274(x)=F13(x)F275(x)F275(x)=F276(x)F276(x)=F272(x)+F277(x)F277(x)=F278(x)F278(x)=F13(x)F279(x)F279(x)=F276(x)F280(x)=F13(x)F281(x)F281(x)=F282(x)+F304(x)F282(x)=F192(x)+F283(x)F283(x)=F284(x)F284(x)=F13(x)F285(x)F285(x)=F282(x)+F286(x)F286(x)=F287(x)+F288(x)F287(x)=F211(x)F288(x)=4F16(x)+F226(x)+F289(x)F289(x)=F13(x)F290(x)F290(x)=F291(x)+F295(x)F291(x)=F287(x)+F292(x)F292(x)=F293(x)F293(x)=F13(x)F294(x)F294(x)=F291(x)F295(x)=F296(x)+F297(x)F296(x)=F237(x)F297(x)=F298(x)F298(x)=F13(x)F299(x)F299(x)=F300(x)F300(x)=F296(x)+F301(x)F301(x)=F302(x)F302(x)=F13(x)F303(x)F303(x)=F300(x)F304(x)=F305(x)+F309(x)F305(x)=3F16(x)+F207(x)+F306(x)F306(x)=F13(x)F307(x)F307(x)=F100(x)+F308(x)F308(x)=F206(x)+F272(x)F309(x)=4F16(x)+F249(x)+F310(x)F310(x)=F13(x)F311(x)F311(x)=F312(x)+F316(x)F312(x)=F305(x)+F313(x)F313(x)=F314(x)F314(x)=F13(x)F315(x)F315(x)=F312(x)F316(x)=F317(x)+F318(x)F317(x)=F259(x)F318(x)=F319(x)F319(x)=F13(x)F320(x)F320(x)=F321(x)F321(x)=F317(x)+F322(x)F322(x)=F323(x)F323(x)=F13(x)F324(x)F324(x)=F321(x)F325(x)=F13(x)F326(x)F326(x)=F327(x)+F349(x)F327(x)=F328(x)+F6(x)F328(x)=F329(x)F329(x)=F13(x)F330(x)F330(x)=F327(x)+F331(x)F331(x)=F332(x)+F333(x)F332(x)=F23(x)F333(x)=2F16(x)+F334(x)+F52(x)F334(x)=F13(x)F335(x)F335(x)=F336(x)+F340(x)F336(x)=F332(x)+F337(x)F337(x)=F338(x)F338(x)=F13(x)F339(x)F339(x)=F336(x)F340(x)=F341(x)+F342(x)F341(x)=F63(x)F342(x)=F343(x)F343(x)=F13(x)F344(x)F344(x)=F345(x)F345(x)=F341(x)+F346(x)F346(x)=F347(x)F347(x)=F13(x)F348(x)F348(x)=F345(x)F349(x)=F195(x)+F350(x)F350(x)=2F16(x)+F351(x)+F75(x)F351(x)=F13(x)F352(x)F352(x)=F353(x)+F375(x)F353(x)=F195(x)+F354(x)F354(x)=F355(x)F355(x)=F13(x)F356(x)F356(x)=F353(x)+F357(x)F357(x)=F358(x)+F359(x)F358(x)=F34(x)F359(x)=3F16(x)+F360(x)+F87(x)F360(x)=F13(x)F361(x)F361(x)=F362(x)+F366(x)F362(x)=F358(x)+F363(x)F363(x)=F364(x)F364(x)=F13(x)F365(x)F365(x)=F362(x)F366(x)=F367(x)+F368(x)F367(x)=F98(x)F368(x)=F369(x)F369(x)=F13(x)F370(x)F370(x)=F371(x)F371(x)=F367(x)+F372(x)F372(x)=F373(x)F373(x)=F13(x)F374(x)F374(x)=F371(x)F375(x)=F376(x)+F377(x)F376(x)=2F16(x)+F167(x)+F30(x)F377(x)=3F16(x)+F110(x)+F378(x)F378(x)=F13(x)F379(x)F379(x)=F380(x)+F384(x)F380(x)=F376(x)+F381(x)F381(x)=F382(x)F382(x)=F13(x)F383(x)F383(x)=F380(x)F384(x)=F385(x)+F386(x)F385(x)=F120(x)F386(x)=F387(x)F387(x)=F13(x)F388(x)F388(x)=F389(x)F389(x)=F385(x)+F390(x)F390(x)=F391(x)F391(x)=F13(x)F392(x)F392(x)=F389(x)