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%I #14 Apr 07 2020 10:42:36
%S 1,22,158,654,1980,4906,10577,20588,37059,62710,100936,155882,232518,
%T 336714,475315,656216,888437,1182198,1548994,2001670,2554496,3223242,
%U 4025253,4979524,6106775,7429526,8972172,10761058,12824554,15193130,17899431,20978352,24467113,28405334,32835110,37801086
%N Number of symmetric 5 X 5 matrices of nonnegative integers with zeros on the main diagonal and every row and column adding to n.
%H Colin Barker, <a href="/A244868/b244868.txt">Table of n, a(n) for n = 0..1000</a>
%H R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F G.f.: (1 + 16*x + 41*x^2 + 16*x^3 + x^4) / (1 - x)^6.
%F From _Colin Barker_, Jan 11 2017: (Start)
%F a(n) = (24 + 94*n + 165*n^2 + 155*n^3 + 75*n^4 + 15*n^5) / 24.
%F 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.
%F (End)
%o (PARI) Vec((1 + 16*x + 41*x^2 + 16*x^3 + x^4) / (1 - x)^6 + O(x^40)) \\ _Colin Barker_, Jan 11 2017
%Y Even bisection of row n=5 of A333351.
%Y Cf. A053494.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jul 07 2014
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