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

0,3

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.

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

Crossrefs

Cf. A279555.

Sequence in context: A153475 A150259 A165531 * A150260 A165532 A165533

Adjacent sequences: A374539 A374540 A374541 * A374543 A374544 A374545

Keyword

nonn,changed

Author

Benjamin Testart, Jul 12 2024

Status

approved