A121285 a(0) = 1; for n>0, a(n) = (n+3)*2^(n-2)-n*binomial(n-1, floor( (n-1)/2 ))-(n-1)*binomial(n-2,floor((n-2)/2)).

1, 1, 2, 4, 10, 22, 54, 120, 284, 626, 1438, 3136, 7044, 15212, 33596, 71952, 156856, 333610, 719886, 1522224, 3257972, 6855476, 14574772, 30541264, 64571400, 134827252, 283727564, 590608960, 1237926184, 2569953496, 5368225848, 11118205088, 23155034480, 47856472218

Offset

0,3

Links

Table of n, a(n) for n=0..33.

A. Bernini, F. Disanto, R. Pinzani and S. Rinaldi, Permutations defining convex permutominoes, J. Int. Seq. 10 (2007) # 07.9.7. [See S_{n+1}.]

F. Disanto and S. Rinaldi, Symmetric convex permutominoes and involutions, PU. M. A., Vol. 22 (2011), No. 1, pp. 39-60. - From N. J. A. Sloane, May 04 2012

Formula

Conjecture: -(n-1)*(3*n^2-27*n+56)*a(n) +2*(n-5)*(3*n^2-12*n+5)*a(n-1) +4*(3*n^3-33*n^2+110*n-118)*a(n-2) -8*(n-3)*(3*n^2-21*n+32)*a(n-3)=0. - R. J. Mathar, Jan 04 2017

Mathematica

Join[{1}, Table[((n+3)2^(n-2))-(n Binomial[n-1, Floor[(n-1)/2]]) -((n-1)Binomial[n-2, Floor[(n-2)/2]]), {n, 50}]] (* Harvey P. Dale, Mar 17 2011 *)

Crossrefs

Sequence in context: A240041 A164990 A348009 * A221536 A290277 A030234

Adjacent sequences: A121282 A121283 A121284 * A121286 A121287 A121288

Keyword

nonn

Author

N. J. A. Sloane, Jul 28 2007

Status

approved