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
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- R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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).
Programs
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PARI
Vec((1 + 16*x + 41*x^2 + 16*x^3 + x^4) / (1 - x)^6 + O(x^40)) \\ Colin Barker, Jan 11 2017
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)