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

%I #8 Jun 12 2020 07:07:17

%S 0,0,0,0,0,0,0,0,0,0,2,54,717,6836,53696,371464,2349981,13915712,

%T 78331106,423642906,2218481677,11313458780,56431232688,276253783984,

%U 1330866576164,6323282609184,29682658858324,137864087593740

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

%H Guttmann, A.J. et al., <a href="https://doi.org/10.1088/0305-4470/33/9/303">Punctured polygons and polyominoes on the square lattice</a>, J. Physics A: Math. and Gen, 33 (9) (2000), 1735-1764.

%F 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

%p 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:

%Y Cf. A055022 (perimeter 4).

%K easy,nonn

%O 0,11

%A _James A. Sellers_, May 31 2000

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Last modified August 11 07:51 EDT 2024. Contains 375059 sequences. (Running on oeis4.)