A259364 a(n) = 18*n^4*(2*n^3 - 23*n^2 + 38*n - 18)^2.
0, 18, 93312, 4737042, 51775488, 263351250, 807055488, 1609827282, 1934917632, 774840978, 691920000, 20514061458, 126428055552, 496767242322, 1543426109568, 4122612551250, 9879830396928, 21788831695122, 44962051370112, 87830997546258, 163819480320000
Offset: 0
Links
- M. P. Delest, Generating functions for column-convex polyominoes, J. Combin. Theory Ser. A 48 (1988), no. 1, pp. 12-31.
- 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
[18*n^4*(2*n^3-23*n^2+38*n-18)^2: n in [0..20]];
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Maple
A259364:=n->18*n^4*(2*n^3 - 23*n^2 + 38*n - 18)^2: seq(A259364(n), n=0..30); # Wesley Ivan Hurt, Apr 12 2017
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Mathematica
Table[18 n^4 (2 n^3 - 23 n^2 + 38 n - 18)^2, {n, 0, 23}] -
Sage
[2*(6*n^5-69*n^4+114*n^3-54*n^2)^2 for n in (0..20)] # Bruno Berselli, Jun 25 2015
Formula
G.f.: 18*x*(1 + 5173*x + 206200*x^2 + 266512*x^3 - 3390686*x^4 + 389794*x^5 + 10761232*x^6 + 5689720*x^7 + 580693*x^8 + 6561*x^9)/(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).