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

0,3

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

Crossrefs

Sequence in context: A363933 A103140 A148320 * A301871 A076866 A151417

Adjacent sequences: A374538 A374539 A374540 * A374542 A374543 A374544

Keyword

nonn,new

Author

Benjamin Testart, Jul 11 2024

Status

approved