A374542 Number of length n inversion sequences avoiding the patterns 102 and 210.

1, 1, 2, 6, 22, 87, 351, 1416, 5681, 22660, 89961, 355924, 1404839, 5536143, 21794634, 85749490, 337271186, 1326421512, 5216761708, 20520185594, 80733298320, 317713643536, 1250674963766, 4924782835110, 19398524629494, 76434881013402, 301270165265954

Offset: 0

Author

Benjamin Testart, Jul 12 2024

Keywords

• nonn

Links

• Benjamin Testart, Table of n, a(n) for n = 0..1600
• Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.

Crossrefs

Cf. A279555.

Formula

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).

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

a(n) ~ 2^(2*n+1)/(3*sqrt(Pi*n)). - Vaclav Kotesovec, Nov 21 2024