A093120 Number of convex polyominoes with an n+1 X n+1 minimal bounding square.

5, 68, 1110, 19010, 329126, 5693968, 98074332, 1680306750, 28638104550, 485731377560, 8202665891316, 137983709713668, 2313146752430780, 38658742468243520, 644327268137066104, 10712855104602481206

Offset: 1

Author

Ralf Stephan, Mar 21 2004

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..825
• V. J. W. Guo and J. Zeng, The number of convex polyominoes and the generating function of Jacobi polynomials, arXiv:math/0403262 [math.CO], 2004.

Crossrefs

Main diagonal of triangle A093118.

Programs

GAP

List([1..20], n-> ((2+n)*Binomial(4*n, 2*n) - 2*n*Binomial(2*n, n)^2)/2); # G. C. Greubel, Jun 26 2019

Magma

[((2+n)*Binomial(4*n, 2*n) - 2*n*Binomial(2*n, n)^2)/2: n in [1..20]]; // G. C. Greubel, Jun 26 2019

Mathematica

a[n_]:= 1/2 (n+2) Binomial[4n, 2n] - n Binomial[2n, n]^2;
Array[a, 16] (* Jean-François Alcover, Jan 15 2019 *)

PARI

a(n) = ((2+n)*binomial(4*n, 2*n) - 2*n*binomial(2*n, n)^2)/2; \\ G. C. Greubel, Jun 26 2019

Sage

[((2+n)*binomial(4*n, 2*n) - 2*n*binomial(2*n, n)^2)/2 for n in (1..20)] # G. C. Greubel, Jun 26 2019

Formula

a(n) = ((2+n)*C(4*n, 2*n) - 2*n*C(2*n, n)^2)/2, n>0.