A307788 Number of valid hook configurations of permutations of [n] that avoid the patterns 231 and 321.

1, 1, 1, 2, 5, 12, 29, 72, 182, 466, 1207, 3158, 8334, 22158, 59299, 159614, 431838, 1173710, 3203244, 8774780, 24118522, 66497316, 183858411, 509670494, 1416231616, 3944027402, 11006186760, 30772507128, 86191006746, 241815195292

Offset

0,4

Comments

Essentially the same as A217333 and A025273. - R. J. Mathar, May 17 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*x^2 - sqrt(1 - 4*x + 4*x^2 - 4*x^3 + 4*x^4)) / (2*x^2).

D-finite with recurrence: (n+2)*a(n) +2*(-2*n-1)*a(n-1) +4*(n-1)*a(n-2) +2*(-2*n+5)*a(n-3) +4*(n-4)*a(n-4)=0. - R. J. Mathar, May 17 2019

Prog

(PARI) my(x='x+O('x^35)); Vec((1 - 2*x + 2*x^2 - sqrt(1 - 4*x + 4*x^2 - 4*x^3 + 4*x^4))/(2*x^2)) \\ Michel Marcus, May 08 2019

Crossrefs

Cf. A307786, A307787.

Sequence in context: A122745 A166292 A010374 * A025273 A217333 A089372

Adjacent sequences: A307785 A307786 A307787 * A307789 A307790 A307791

Keyword

nonn

Author

Colin Defant, Apr 28 2019

Status

approved