A374541 Number of length n inversion sequences avoiding the patterns 000 and 102.
1, 1, 2, 5, 14, 40, 121, 373, 1181, 3796, 12391, 40902, 136408, 458735, 1554220, 5299505, 18172874, 62630809, 216821747, 753646690, 2629153881, 9202404515, 32307100270, 113735363082, 401418269205, 1420094167064, 5034768842706, 17886133630919, 63660082770995
Offset: 0
Keywords
Links
- Benjamin Testart, Table of n, a(n) for n = 0..1700
- Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.
Formula
G.f. F(x) is algebraic with minimal polynomial x^4*F(x)^4 - 2x^3*(x - 1)*F(x)^3 + x*(x^3 - 2x^2 + 4x - 1)*F(x)^2 - (2x^2 - 2x + 1)*F(x) + 1.
D-finite with recurrence +6*n*(2*n+3)*(n+1)*( 115902037476970209609532651797*n^2 -804118437163528377413428024057*n +1144854118031312841899645712338)*a(n) -n*(10309262772112485980996703347969*n^4 -57162589371549435280943274602278*n^3 +12807374239180509091028006690617*n^2 +84356126163879743293193632901956*n +18185483948089898030087482673436)*a(n-1) +(-15899321872218080521626271255801*n^5 +190505272362978094637444778237788*n^4 -742400385313337115745145921980901*n^3 +1019298552408570449091756485004142*n^2 -511271776606699338659085562591944*n +73466790571048631419529002789056)*a(n-2) +2*(56936644898147528366574504466487*n^5 -675905645915443170938754654383314*n^4 +3075899243769705758269387104723700*n^3 -7058855512159881677801564918535971*n^2 +8329069356873697552872190210428006*n -4010067281702663096010201516806496)*a(n-3) +6*(19715522268053782894372158603554*n^5 -223873172486730362151444782585359*n^4 +768950708146310213860389653514276*n^3 -322203528457905963286300676101927*n^2 -2652956139033073818620652982999090*n +3431951459827641350270606566580448)*a(n-4) +6*(-28783069213038773900872833291016*n^5 +660483392782304911307979323624655*n^4 -5710025389637531078101745800393964*n^3 +23348742745530285114652064145006971*n^2 -45038913957699867856392343980190102*n +32395575988873081222604689446753408)*a(n-5) +2*(-52125561607675742290830728101036*n^5 +1096826483115921591413340938785277*n^4 -8964613839701931786202789630678637*n^3 +35452105313339403598394068417163428*n^2 -67298808848110422804027907099733868*n +48130119233409879884308835283522912)*a(n-6) +2*(1335874141771041425279542675228*n^5 -89624832525830246822350394263871*n^4 +1285352819570898563452386493037618*n^3 -7379532769264495115767883376023869*n^2 +18431453516658889307737544610500190*n -16496221432359357241460726610441888)*a(n-7) +4*(n-8)*(11825669122095960407967481054039*n^4 -203980551515992382593286563968000*n^3 +1240787898462597866259674648717159*n^2 -3106873194313435459725804877098966*n +2614835102425910549478511336348776)*a(n-8) -24*(n-5)*(n-8)*(n-9)*(474105943175860040316559647091*n^2 -2672180534791313338630701561778*n +3260085783436342074450617685024)*a(n-9)=0. - R. J. Mathar, Jul 12 2024