A055024 Number of 1-punctured staircase polygons (by perimeter) with a hole of perimeter 6.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 54, 717, 6836, 53696, 371464, 2349981, 13915712, 78331106, 423642906, 2218481677, 11313458780, 56431232688, 276253783984, 1330866576164, 6323282609184, 29682658858324, 137864087593740

Offset

0,11

Links

Table of n, a(n) for n=0..27.

Guttmann, A.J. et al., Punctured polygons and polyominoes on the square lattice, J. Physics A: Math. and Gen, 33 (9) (2000), 1735-1764.

Formula

D-finite with recurrence +n*(n-10)*(7922123*n -106081693)*a(n) +2*(-100307698*n^3 +2258882361*n^2 -14191179053*n +19100093430)*a(n-1) +16*(76541329*n^3 -1663392372*n^2 +11013283712*n -21512745186)*a(n-2) -32*(n-7) *(34309603*n -256074474)*(2*n-13)*a(n-3)=0. - R. J. Mathar, Jun 12 2020

Maple

gf := (1 - 26*x + 228*x^2 - 906*x^3 + 1709*x^4 - 1378*x^5 + 322*x^6)/(2*(1 - 4*x)^(5/2)) - (32*x^6 - 404*x^5 + 815*x^4 - 586*x^3 + 182*x^2 - 24*x + 1)/(2*(1 - 4*x)^2): s := series(gf, x, 50): for i from 0 to 50 do printf(`%d, `, coeff(s, x, i)) od:

Crossrefs

Cf. A055022 (perimeter 4).

Sequence in context: A113028 A200195 A202739 * A057411 A157058 A305693

Adjacent sequences: A055021 A055022 A055023 * A055025 A055026 A055027

Keyword

easy,nonn

Author

James A. Sellers, May 31 2000

Status

approved