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

Author

Colin Defant, Apr 28 2019

Keywords

• nonn

Comments

Essentially the same as A217333 and A025273. - R. J. Mathar, May 17 2019

Links

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

Crossrefs

Cf. A307786, A307787.

Programs

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

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