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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). 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.)