A307789 - OEIS

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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

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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