A244868 Number of symmetric 5 X 5 matrices of nonnegative integers with zeros on the main diagonal and every row and column adding to n.

1, 22, 158, 654, 1980, 4906, 10577, 20588, 37059, 62710, 100936, 155882, 232518, 336714, 475315, 656216, 888437, 1182198, 1548994, 2001670, 2554496, 3223242, 4025253, 4979524, 6106775, 7429526, 8972172, 10761058, 12824554, 15193130, 17899431, 20978352, 24467113, 28405334, 32835110, 37801086

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

G.f.: (1 + 16*x + 41*x^2 + 16*x^3 + x^4) / (1 - x)^6.

From Colin Barker, Jan 11 2017: (Start)

a(n) = (24 + 94*n + 165*n^2 + 155*n^3 + 75*n^4 + 15*n^5) / 24.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.

(End)

Prog

(PARI) Vec((1 + 16*x + 41*x^2 + 16*x^3 + x^4) / (1 - x)^6 + O(x^40)) \\ Colin Barker, Jan 11 2017

Crossrefs

Even bisection of row n=5 of A333351.

Cf. A053494.

Sequence in context: A041934 A027943 A224257 * A223913 A189416 A224185

Adjacent sequences: A244865 A244866 A244867 * A244869 A244870 A244871

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 07 2014

Status

approved