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A005650 Number of "magic squares" of order n (see comment line for exact definition).
(Formerly M2704)
2
1, 1, 3, 7, 47, 207, 2249, 14501, 216273, 1830449, 34662523, 362983263, 8330310559, 103938238111, 2801976629841, 40574514114061, 1256354802202337, 20708839411614753, 724160187180691379, 13386284447024070647 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 16 00:11 EST 2018. Contains 317252 sequences. (Running on oeis4.)