Av(1234, 1324, 2143, 2413, 3142)
View Raw Data
Generating Function
2x12x4+x3x2+3x1
Counting Sequence
1, 1, 2, 6, 19, 55, 156, 444, 1269, 3629, 10374, 29650, 84743, 242211, 692288, ...
Implicit Equation for the Generating Function
(2x4+x3x2+3x1)F(x)2x+1=0
Recurrence
a(0)=1
a(1)=1
a(2)=2
a(3)=6
a(n+4)=2a(n)+a(n+1)a(n+2)+3a(n+3),n4
Explicit Closed Form
2068379(((213(57135139101)(35713+85)13+(4272233571323251392233232)(35713+85)23+4965713101)256213(571341)(35713+85)13+51392+(192233571+827223)(35713+85)23479640213(3+9571571)(35713+85)13101+419685(33695713997)223(35713+85)23404+282240571101)483256213(571341)(35713+85)13+51392+(192233571+827223)(35713+85)23+(95713+255)223(35713+85)23+1536213(35713+85)137296+11694083256213(571341)(35713+85)13+51392+(192233571+827223)(35713+85)231018840724480101+((35713+85)23(7080431018292571101)+255808(3335713997)223(35713+85)13101)(195713+827)(35713+85)23+(12822335715248223)(35713+85)13+25696213)(3394838200320(48768213(571341)(35713+85)13+154176+(572233571+2481223)(35713+85)23+(95713255)223(35713+85)231536213(35713+85)13+729619219768213(571341)(35713+85)13+154176+(572233571+2481223)(35713+85)2360480+(85(35713+85)23256(340+125713)13)(575713+2481)(35713+85)23+384223(571341)(35713+85)13+770882131935360+(108495713+472217)(35713+85)23+73088223(571341)(35713+85)13+14672416213(35713+85)2321504018)n20479+((((5767671223655328+3754712233571655328)(35713+85)23+(96129571321320479+472616721320479)(35713+85)13478416571320479)256213(571341)(35713+85)13+51392+(192233571+827223)(35713+85)23383652045(31223875711217943)223(35713+85)2381916+522327960213(3+1091571207273)(35713+85)132047927115200057120479)483256213(571341)(35713+85)13+51392+(192233571+827223)(35713+85)23+(95713+255)223(35713+85)23+1536213(35713+85)1372966349885443256213(571341)(35713+85)13+51392+(192233571+827223)(35713+85)2320479+((703674571204793429426320479)(35713+85)2328559136(9423571297491+3)223(35713+85)1320479)(195713+827)(35713+85)23+(12822335715248223)(35713+85)13+2569621367639320(57132004218947)223(35713+85)232047936865821081602047975237120213(571356529311)(35713+85)1320479)(48768213(571341)(35713+85)13+154176+(572233571+2481223)(35713+85)23+(95713255)223(35713+85)231536213(35713+85)13+729619219768213(571341)(35713+85)13+154176+(572233571+2481223)(35713+85)2360480+(85(35713+85)23256(340+125713)13)(575713+2481)(35713+85)23+384223(571341)(35713+85)13+770882131935360+(108495713+472217)(35713+85)23+73088223(571341)(35713+85)13+14672416213(35713+85)2321504018)n+(((299171((27087I2991713712333299171)571+I312349017299171)223(35713+85)231310656((66994320479+381I20479)571+I3288811820479)213(35713+85)135930003(3561157174125+I)20479)256213(571341)(35713+85)13+51392+(192233571+827223)(35713+85)232451645((I31552617783)571216081I7783+125791337783)223(35713+85)2316383232760((I3+183213)57121123I13155312313)213(35713+85)1320479+3632247360I2047917972640057120479)483256213(571341)(35713+85)13+51392+(192233571+827223)(35713+85)23+(95713+255)223(35713+85)23+1536213(35713+85)1372961597443(I571+20727326)256213(571341)(35713+85)13+51392+(192233571+827223)(35713+85)2320479+(((71305472047949299I320479)57159596983320479950715I20479)(35713+85)23+220080(35713+85)13((I3+453934585)571217551I4585465422134585)22320479)(195713+827)(35713+85)23+(12822335715248223)(35713+85)13+25696213+757591380((8947I66807+89473200421)571+I31)223(35713+85)23204793686582108160204796837747840((311I18843311356529)571+I3+1)213(35713+85)1320479)(I48768213(571341)(35713+85)13+154176+(572233571+2481223)(35713+85)23+(95713+255)223(35713+85)23+1536213(35713+85)137296192+19768213(571341)(35713+85)13+154176+(572233571+2481223)(35713+85)2360480+(85(35713+85)23+256(340+125713)13)(575713+2481)(35713+85)23+384223(571341)(35713+85)13+770882131935360(108495713+472217)(35713+85)23+73088223(571341)(35713+85)13+14672416213(35713+85)2321504018)n+(I48768213(571341)(35713+85)13+154176+(572233571+2481223)(35713+85)23+(95713+255)223(35713+85)23+1536213(35713+85)137296192+19768213(571341)(35713+85)13+154176+(572233571+2481223)(35713+85)2360480+(85(35713+85)23+256(340+125713)13)(575713+2481)(35713+85)23+384223(571341)(35713+85)13+770882131935360(108495713+472217)(35713+85)23+73088223(571341)(35713+85)13+14672416213(35713+85)2321504018)n(((299171((27087I299171+3712333299171)571+I3+12349017299171)223(35713+85)231310656+213((381I2047966994320479)571+I3+288811820479)(35713+85)13+5930003(3561157174125+I)20479)256213(571341)(35713+85)13+51392+(192233571+827223)(35713+85)23+2451645((I3+1552617783)571216081I7783125791337783)223(35713+85)23163832+32760213((I3183213)57121123I13+155312313)(35713+85)13204793632247360I2047917972640057120479)483256213(571341)(35713+85)13+51392+(192233571+827223)(35713+85)23+(95713+255)223(35713+85)23+1536213(35713+85)137296+1597443(I57120727326)256213(571341)(35713+85)13+51392+(192233571+827223)(35713+85)2320479+(((713054720479+49299I320479)57159596983320479+950715I20479)(35713+85)23220080(35713+85)13((I3453934585)571217551I4585+465422134585)22320479)(195713+827)(35713+85)23+(12822335715248223)(35713+85)13+25696213757591380((8947I6680789473200421)571+I3+1)223(35713+85)2320479368658210816020479+6837747840213((311I18843+311356529)571+I31)(35713+85)1320479))120051316732832671334400

This specification was found using the strategy pack "Point Placements" and has 72 rules.

Found on January 18, 2022.

Finding the specification took 1 seconds.

Copy to clipboard:

View tree on standalone page.

Copy 72 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)=F16(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)F15(x)=F13(x)F4(x)F16(x)=F17(x)+F2(x)F17(x)=F18(x)+F19(x)+F57(x)F18(x)=0F19(x)=F20(x)F4(x)F20(x)=F21(x)+F28(x)F21(x)=F22(x)+F25(x)F22(x)=F23(x)F23(x)=F24(x)F4(x)F24(x)=F1(x)+F4(x)F25(x)=F26(x)F26(x)=F27(x)F4(x)F27(x)=F4(x)F28(x)=F29(x)+F51(x)F29(x)=F18(x)+F19(x)+F30(x)F30(x)=F31(x)F4(x)F31(x)=F2(x)+F32(x)F32(x)=F18(x)+F33(x)+F50(x)F33(x)=F34(x)F4(x)F34(x)=F35(x)+F37(x)F35(x)=F36(x)+F4(x)F36(x)=F26(x)F37(x)=F32(x)+F38(x)F38(x)=2F18(x)+F39(x)+F48(x)F39(x)=F4(x)F40(x)F40(x)=F41(x)+F44(x)F41(x)=F42(x)F42(x)=F4(x)F43(x)F43(x)=F4(x)F44(x)=F45(x)F45(x)=2F18(x)+F39(x)+F46(x)F46(x)=F4(x)F47(x)F47(x)=F32(x)F48(x)=F4(x)F49(x)F49(x)=F32(x)F50(x)=F2(x)F4(x)F51(x)=2F18(x)+F48(x)+F52(x)F52(x)=F4(x)F53(x)F53(x)=F54(x)+F55(x)F54(x)=F42(x)F55(x)=F56(x)F56(x)=2F18(x)+F46(x)+F52(x)F57(x)=F4(x)F58(x)F58(x)=F59(x)+F64(x)F59(x)=F2(x)+F60(x)F60(x)=F18(x)+F33(x)+F61(x)F61(x)=F4(x)F62(x)F62(x)=F2(x)+F63(x)F63(x)=F61(x)F64(x)=F65(x)+F71(x)F65(x)=F66(x)F66(x)=F4(x)F67(x)F67(x)=F62(x)+F68(x)F68(x)=F65(x)+F69(x)F69(x)=F70(x)F70(x)=F4(x)F68(x)F71(x)=F70(x)