A307789 Number of valid hook configurations of permutations of [n] that avoid the patterns 231 and 1243.

1, 1, 1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584, 1201917, 3492117, 10165779, 29643870, 86574831, 253188111, 741365049, 2173243128, 6377181825, 18730782252, 55062586341, 161995031226, 476941691177, 1405155255055

Offset

0,4

Comments

Essentially the same as A005773. - R. J. Mathar, May 06 2019

Links

Table of n, a(n) for n=0..29.

Colin Defant, Motzkin intervals and valid hook configurations, arXiv preprint arXiv:1904.10451 [math.CO], 2019.

Formula

G.f.: 1 + 2*x^2/(3*x - 1 + sqrt(1 - 2*x - 3*x^2)).

D-finite with recurrence: +(-n+1)*a(n) +2*(n-1)*a(n-1) +3*(n-3)*a(n-2)=0. - R. J. Mathar, Jan 27 2020

a(n) = Sum_{k=0..n-2} A064189(n-2,k) for n>=2. - Alois P. Heinz, Aug 29 2022

Crossrefs

Cf. A005773, A064189.

Sequence in context: A085810 A355040 A235611 * A005773 A022855 A091190

Adjacent sequences: A307786 A307787 A307788 * A307790 A307791 A307792

Keyword

nonn

Author

Colin Defant, Apr 28 2019

Status

approved