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A055024 Number of 1-punctured staircase polygons (by perimeter) with a hole of perimeter 6. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,11
LINKS
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
KEYWORD
easy,nonn
AUTHOR
James A. Sellers, May 31 2000
STATUS
approved

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Last modified July 14 22:45 EDT 2024. Contains 374323 sequences. (Running on oeis4.)