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

Author

Colin Defant, Apr 28 2019

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A005773, A064189.

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