%I #19 Dec 20 2023 21:18:57

%S 18,1080,99248,6710160,312975306,8820400232,155825544448,

%T 1902742912440,17422385919290,126966804496576,769002076834992,

%U 3997219502682952,18271131867527266,74845992604425840,278918348891883520,957055146953124368,3053791953265318722

%N Number of n X n arrays of squares of integers summing to 10.

%H R. H. Hardin, <a href="/A159379/b159379.txt">Table of n, a(n) for n=2..100</a>

%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (21, -210, 1330, -5985, 20349, -54264, 116280, -203490, 293930, -352716, 352716, -293930, 203490, -116280, 54264, -20349, 5985, -1330, 210, -21, 1).

%F Empirical G.f.: -2*x^2*(1+x)*(9 + 342*x + 39832*x^2 + 2374574*x^3 + 93413104*x^4 + 1672161938*x^5 + 12313058136*x^6 + 40002238314*x^7 + 59444070702*x^8 + 40002238314*x^9 + 12313058136*x^10 + 1672161938*x^11 + 93413104*x^12 + 2374574*x^13 + 39832*x^14 + 342*x^15 + 9*x^16)/(-1+x)^21. - _Vaclav Kotesovec_, Nov 30 2012

%F a(n) = multinomial(n^2,1,1,n-2) + multinomial(n^2,2,2,n^2-4) + multinomial(n^2,1,6,n^2-7) + binomial(n^2,10)

%F = (n^20 - 45*n^18 + 870*n^16 - 4410*n^14 - 42567*n^12 + 612675*n^10 - 2073520*n^8 + 1569060*n^6 + 5744016*n^4 - 5806080*n^2)/3628800,

%F corresponding to the ways of obtaining 10 as a sum of n^2 squares:

%F 9 + 1 + (n^2-2)*0, 2*4 + 2*1 + (n^2-4)*0, 4 + 6*1 + (n^2 - 7)*0, and 10*1 + (n^2 - 10)*0. - _Robert Israel_, Dec 20 2023

%K nonn,easy

%O 2,1

%A _R. H. Hardin_, Apr 11 2009