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, and R. Hemmecke, Polyhedral Cones of Magic Cubes and Squares, arXiv:math/0201108 [math.CO], 2002.
Maya Ahmed, Jesús 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
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