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A070212 Number of 5 X 5 pandiagonal magic squares with sum n. 2
1, 10, 55, 220, 715, 2001, 4995, 11385, 24090, 47905, 90376, 162955, 282490, 473110, 768570, 1215126, 1875015, 2830620, 4189405, 6089710, 8707501, 12264175, 17035525, 23361975, 31660200, 42436251, 56300310, 73983205, 96354820, 124444540, 159463876, 202831420, 256200285, 321488190 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In contrast to other definitions, a magic square may contain here any nonnegative integers, not necessarily distinct. For example, the 10 solutions for n = 1 are the 10 permutation matrices of size 5 X 5 which are pandiagonal in the sense that any of the 10 (principal or broken) diagonals has exactly one 1 and four 0's. - M. F. Hasler, Oct 23 2018

LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..5000

M. Ahmed, J. De Loera, R. Hemmecke, Polyhedral Cones of Magic Cubes and Squares, arXiv:math/0201108 [math.CO], 2002.

Maya Ahmed, Jesus De Loera and Raymond Hemmecke, Polyhedral cones of magic cubes and squares, in Discrete and Computational Geometry, Springer, Berlin, 2003, pp. 25-41.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Index entries related to magic squares.

FORMULA

a(n) = (1/8064) * (n+4)*(n+3)*(n+2)*(n+1)*(n^2+5n+8)*(n^2+5n+42).

G.f.: -(x^4+x^3+x^2+x+1) / (x-1)^9. [Colin Barker, Dec 10 2012]

MAPLE

seq(coeff(series(-(x^4+x^3+x^2+x+1)/(x-1)^9, x, n+1), x, n), n = 0 .. 35); # Muniru A Asiru, Oct 23 2018

MATHEMATICA

LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 10, 55, 220, 715, 2001, 4995, 11385, 24090}, 40] (* Harvey P. Dale, Mar 13 2018 *)

PROG

(PARI) apply( A070212(n)=1/8064*(n+4)*(n+3)*(n+2)*(n+1)*(n^2+5*n+8)*(n^2+5*n+42), [0..20]) \\ Edited by M. F. Hasler, Oct 23 2018

(GAP) a:=[1, 10, 55, 220, 715, 2001, 4995, 11385, 24090];;  for n in [10..36] do a[n]:=9*a[n-1]-36*a[n-2]+84*a[n-3]-126*a[n-4]+126*a[n-5]-84*a[n-6]+36*a[n-7]-9*a[n-8]+a[n-9]; od; a; # Muniru A Asiru, Oct 23 2018

CROSSREFS

Cf. A027567, A014820, A111158, A053494.

Sequence in context: A127761 A244871 A162617 * A289380 A008502 A008492

Adjacent sequences:  A070209 A070210 A070211 * A070213 A070214 A070215

KEYWORD

nonn,easy

AUTHOR

Sharon Sela (sharonsela(AT)hotmail.com), May 07 2002

EXTENSIONS

More terms from Benoit Cloitre, May 12 2002

More terms from M. F. Hasler, Oct 23 2018

STATUS

approved

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)