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A093120
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Number of convex polyominoes with an n+1 X n+1 minimal bounding square.
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2
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5, 68, 1110, 19010, 329126, 5693968, 98074332, 1680306750, 28638104550, 485731377560, 8202665891316, 137983709713668, 2313146752430780, 38658742468243520, 644327268137066104, 10712855104602481206
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = ((2+n)*C(4*n, 2*n) - 2*n*C(2*n, n)^2)/2, n>0.
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MATHEMATICA
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a[n_]:= 1/2 (n+2) Binomial[4n, 2n] - n Binomial[2n, n]^2;
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PROG
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(PARI) a(n) = ((2+n)*binomial(4*n, 2*n) - 2*n*binomial(2*n, n)^2)/2; \\ G. C. Greubel, Jun 26 2019
(Magma) [((2+n)*Binomial(4*n, 2*n) - 2*n*Binomial(2*n, n)^2)/2: n in [1..20]]; // G. C. Greubel, Jun 26 2019
(Sage) [((2+n)*binomial(4*n, 2*n) - 2*n*binomial(2*n, n)^2)/2 for n in (1..20)] # G. C. Greubel, Jun 26 2019
(GAP) List([1..20], n-> ((2+n)*Binomial(4*n, 2*n) - 2*n*Binomial(2*n, n)^2)/2) # G. C. Greubel, Jun 26 2019
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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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