A374541 - OEIS

%I #15 Jul 12 2024 13:01:56

%S 1,1,2,5,14,40,121,373,1181,3796,12391,40902,136408,458735,1554220,

%T 5299505,18172874,62630809,216821747,753646690,2629153881,9202404515,

%U 32307100270,113735363082,401418269205,1420094167064,5034768842706,17886133630919,63660082770995

%N Number of length n inversion sequences avoiding the patterns 000 and 102.

%H Benjamin Testart, <a href="/A374541/b374541.txt">Table of n, a(n) for n = 0..1700</a>

%H Benjamin Testart, <a href="https://arxiv.org/abs/2407.07701">Completing the enumeration of inversion sequences avoiding one or two patterns of length 3</a>, arXiv:2407.07701 [math.CO], 2024.

%F 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.

%F 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

%K nonn

%O 0,3

%A _Benjamin Testart_, Jul 11 2024