A057051 Number of polyominoes of 2n-1 cells that span an n X n square.

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

Offset

1,3

Links

Table of n, a(n) for n=1..27.

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