A005650 Number of "magic squares" of order n (see comment line for exact definition). (Formerly M2704)

1, 1, 3, 7, 47, 207, 2249, 14501, 216273, 1830449, 34662523, 362983263, 8330310559, 103938238111, 2801976629841, 40574514114061, 1256354802202337, 20708839411614753, 724160187180691379, 13386284447024070647

Offset

0,3

Comments

This is the number of n X n square arrays with nonnegative integer entries in which every row and column add to 2 (A000681) normalized by dividing by n!/2^floor(n/2).

References

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 125, #25, A_n.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for sequences related to magic squares

Formula

a(n) = A000681(n)*2^floor(n/2)/n!.

a(n) ~ 2^(floor(n/2) + 1/2) * n^n * exp(1/2-n). - Vaclav Kotesovec, Aug 13 2013

Recurrence: a(n) = (2*n^2 - 4*n + 1)*a(n-2) - (n-3)*n*a(n-4). - Vaclav Kotesovec, Aug 13 2013

Mathematica

A000681[n_] := Sum[((2*i)!*n!^2)/(2^i*(i!^2*(n - i)!)), {i, 0, n}]/2^n;
a[n_] := A000681[n]*2^Floor[n/2]/n!;
Table[a[n], {n, 0, 19}]
(* Jean-François Alcover, Mar 14 2012, after Shanzhen Gao *)

Crossrefs

Sequence in context: A074714 A064457 A318087 * A020754 A052381 A219877

Adjacent sequences: A005647 A005648 A005649 * A005651 A005652 A005653

Keyword

nonn,nice,easy

Author

N. J. A. Sloane, Simon Plouffe

Extensions

More terms from Vladeta Jovovic, Feb 11 2001

Status

approved