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 A057051 Number of polyominoes of 2n-1 cells that span an n X n square. 1
 1, 1, 6, 18, 73, 255, 950, 3473, 13006, 48840, 185353, 706404, 2706608, 10404625, 40126430, 155133811, 601119492, 2333671638, 9075290555, 35345525798, 137847145330, 538258922839, 2104101413400, 8233434921693, 32247613423563, 126410623214720, 495918571702575 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS D. E. Knuth, Animals in a cage, Problem 10875, Amer. Math. Monthly, 110 (March 2003), 243-245. R. J. Mathar, Corrigendum to "Polyomino Enumeration Results (Parkin et al, SIAM Fall Meeting 1967)" viXra:1905.0474 (2019) R. Parkin, L. J. Lander, and D. R. Parkin, Polyomino Enumeration Results, presented at SIAM Fall Meeting, 1967) and accompanying letter from T. J. Lander (annotated scanned copy) page 9 (incorrect at n=15). FORMULA See Maple code. MAPLE A057051 := proc(n) if n mod 2 = 0 then binomial(2*n-2, n-1)+2^(n-2)-(3*n^2-2*n+8)/8; else binomial(2*n-2, n-1)+2^(n-2)-(3*n^2-4*n+9)/8+(1/2)*binomial(n-1, (n-1)/2); end if; end proc; MATHEMATICA f[n_] := If[EvenQ[n], Binomial[2n-2, n-1] + 2^(n-2) - (3n^2-2n+8)/8, Binomial[2n-2, n-1] + 2^(n-2) - (3n^2-4n+9)/8 + (1/2) Binomial[n-1, (n-1)/2]]; Table[f[n], {n, 1, 27}] (* Jean-François Alcover, Mar 18 2017, translated from Maple *) CROSSREFS Sequence in context: A129796 A129790 A121156 * A318069 A332939 A299412 Adjacent sequences:  A057048 A057049 A057050 * A057052 A057053 A057054 KEYWORD nonn AUTHOR N. J. A. Sloane, Mar 08 2003 STATUS approved

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Last modified March 28 05:04 EDT 2020. Contains 333073 sequences. (Running on oeis4.)