A259395 a(n) = -3*n^2*(n-1)^4*(n+1)*(11*n^3+49*n^2-439*n+171).
0, 0, 15228, 705024, 1885680, -66355200, -792382500, -4986842112, -22516232256, -81696522240, -252908835300, -693126720000, -1723987588752, -3961019252736, -8517765880260, -17315965900800, -33541737120000, -62298041352192, -111515651966916, -193198552634880
Offset: 0
Links
- M. P. Delest, Generating functions for column-convex polyominoes, J. Combin. Theory Ser. A 48 (1988), no. 1, pp. 12-31. See expression D in Theorem 16 page 29.
- Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
Programs
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Magma
[-3*n^2*(n-1)^4*(n+1)*(11*n^3+49*n^2-439*n+171): n in [0..20]];
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Maple
A259395:=n->-3*n^2*(n-1)^4*(n+1)*(11*n^3+49*n^2-439*n+171): seq(A259395(n), n=0..25); # Wesley Ivan Hurt, Jun 29 2015
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Mathematica
Table[-3 n^2 (n - 1)^4 (n + 1) (11 n^3 + 49 n^2 - 439 n + 171), {n, 0, 23}] LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{0,0,15228,705024,1885680,-66355200,-792382500,-4986842112,-22516232256,-81696522240,-252908835300},20] (* Harvey P. Dale, Jul 07 2025 *)
Formula
G.f.: 324*x^2*(47+1659*x - 15531*x^2 - 156895*x^3 - 216255*x^4 - 17547*x^5 + 31451*x^6 + 3471*x^7) / (1-x)^11.
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11).