A374542 - OEIS

%I #13 Nov 21 2024 03:10:17

%S 1,1,2,6,22,87,351,1416,5681,22660,89961,355924,1404839,5536143,

%T 21794634,85749490,337271186,1326421512,5216761708,20520185594,

%U 80733298320,317713643536,1250674963766,4924782835110,19398524629494,76434881013402,301270165265954

%N Number of length n inversion sequences avoiding the patterns 102 and 210.

%H Benjamin Testart, <a href="/A374542/b374542.txt">Table of n, a(n) for n = 0..1600</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: ((4*x - 1) * (4*x^4 - 22*x^3 + 25*x^2 - 9*x + 1) - (2*x - 1) * (x^2 - 5*x + 1) * (2*x^2 - 4*x + 1) * (1-4*x)^(1/2)) / (2*x^3 * (4*x - 1) * (x - 1)^2).

%F D-finite with recurrence -(n+3)*(1514*n-13441)*a(n) +(16281*n^2-104929*n-159699)*a(n-1) +(-54702*n^2+377288*n-136533)*a(n-2) +(60299*n^2-430394*n+520290)*a(n-3) -6*(2*n-7)*(1697*n-7015)*a(n-4) +30*(-702*n+3361)=0. - _R. J. Mathar_, Jul 12 2024

%F a(n) ~ 2^(2*n+1)/(3*sqrt(Pi*n)). - _Vaclav Kotesovec_, Nov 21 2024

%Y Cf. A279555.

%K nonn,changed

%O 0,3

%A _Benjamin Testart_, Jul 12 2024