A122122 a(0) = 1; for n>0, a(n) = 2*(n+2)*4^(n-2)-(n/4)*((3-4*n)/(1-2*n))*binomial(2*n,n).

1, 1, 3, 13, 62, 301, 1450, 6882, 32156, 148093, 673394, 3028246, 13487908, 59577298, 261255012, 1138378276, 4932592056, 21267076637, 91289277250, 390312067278, 1662864320084, 7061599302214, 29900598469548, 126269921669660, 531939145476232, 2235903406963506

Offset

0,3

Links

Table of n, a(n) for n=0..25.

A. Bernini, F. Disanto, R. Pinzani and S. Rinaldi, Permutations defining convex permutominoes, J. Int. Seq. 10 (2007) # 07.9.7. [See C^{~}_{n}.]

Filippo Disanto, Andrea Frosini and Simone Rinaldi, Renzo Pinzani, The Combinatorics of Convex Permutominoes, Southeast Asian Bulletin of Mathematics (2008) 32: 883-912.

F. Disanto and S. Rinaldi, Symmetric convex permutominoes and involutions, PU. M. A., Vol. 22 (2011), No. 1, pp. 39-60.

I. Fanti, A. Frosini, E. Grazzini, R. Pinzani and S. Rinaldi, Characterization and enumeration of some classes of permutominoes, PU. M. A., Vol. 18 (2007), No. 3-4, pp. 265-290.

Formula

Conjecture: n*(4*n^2-21*n+19)*a(n) +2*(-16*n^3+80*n^2-77*n+3)*a(n-1) +8*(2*n-3)*(4*n^2-13*n+2)*a(n-2)=0. - R. J. Mathar, Jan 04 2017

Conjecture: n*a(n) +2*(-4*n-1)*a(n-1) +72*a(n-2) +32*(4*n-15)*a(n-3) +128*(-2*n+7)*a(n-4)=0. - R. J. Mathar, Jan 04 2017

Prog

(PARI) a(n) = if (n==0, 1, 2*(n+2)*4^(n-2)-(n/4)*((3-4*n)/(1-2*n))*binomial(2*n, n)); \\ Michel Marcus, Nov 02 2015

Crossrefs

Sequence in context: A246689 A355987 A141786 * A093424 A186242 A367060

Adjacent sequences: A122119 A122120 A122121 * A122123 A122124 A122125

Keyword

nonn

Author

N. J. A. Sloane, Jul 28 2007

Extensions

Missing a(0) inserted by Michel Marcus, Jun 13 2022

Status

approved