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A126765
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a(n) = number of L-convex polyominoes inscribed in an (n+1) X (n+1) box.
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3
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1, 5, 42, 402, 4070, 42510, 452900, 4891988, 53376966, 586921790, 6493225772, 72192371100, 805935279708, 9028253155628, 101433497725320, 1142504966609512, 12897113121607750, 145870996300613406, 1652690392388658012, 18753389068268792780, 213091273336786301940
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OFFSET
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0,2
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COMMENTS
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See A126764 for definition of L-convex.
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REFERENCES
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G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of L-convex polyominoes, European J. Combin. 28 (2007), no. 6, 1724-1741.
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LINKS
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FORMULA
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G.f.: (1/2) * sqrt( (2+5*x-2*x^2+(2-x)*sqrt(1-12*x+4*x^2) )/ (1-12*x+4*x^2) ).
a(n) ~ 2^(n-9/4) * (3+2*sqrt(2))^(n+1) / sqrt((1+sqrt(2))*Pi*n). - Vaclav Kotesovec, Feb 16 2015
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MAPLE
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a:= proc(n) option remember; `if`(n<2, 4*n+1, (12*(4*n-1)*(2*n-1)*(n-1)^2*
a(n-1)-4*(n-2)*(2*n-3)*n*(4*n+1)*a(n-2))/((4*n-3)*(2*n-1)*n*(n-1)))
end:
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MATHEMATICA
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CoefficientList[Series[(1/2)Sqrt[(2+5x-2x^2+(2-x)Sqrt[1-12x+4x^2])/ (1-12x+4x^2)], {x, 0, 20}], x] (* Harvey P. Dale, Jun 14 2011 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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