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%I #19 Feb 17 2022 20:55:27
%S 5,135,1836,12675,58941,211925,635440,1663821,3921325,8495531,
%T 17179020,32795295,59626581,103962825,174792896,284660665,450710325,
%U 695946991,1050740300,1554600411,2258257485,3226077405,4538848176,6296973125,8624108701,11671286355
%N Number of n X n arrays of squares of integers summing to 4.
%C Each array either has four 1's or one 4, and all other elements 0. - _Robert Israel_, Jun 19 2018
%H R. H. Hardin, <a href="/A159355/b159355.txt">Table of n, a(n) for n=2..100</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F Empirical: n^2*(n^2+1)*(n^4-7*n^2+18)/24. - _R. J. Mathar_, Aug 11 2009
%F From _Robert Israel_, Jun 19 2018: (Start)
%F Empirical formula confirmed.
%F a(n) = binomial(n^2,4)+n^2 = A014626(n^2).
%F (End)
%F From _Colin Barker_, Jun 19 2018: (Start)
%F G.f.: x^2*(5 + 90*x + 801*x^2 + 591*x^3 + 252*x^4 - 88*x^5 + 37*x^6 - 9*x^7 + x^8) / (1 - x)^9.
%F 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) for n>10.
%F (End)
%p seq(binomial(n^2,4)+n^2, n=2..100);
%o (PARI) Vec(x^2*(5 + 90*x + 801*x^2 + 591*x^3 + 252*x^4 - 88*x^5 + 37*x^6 - 9*x^7 + x^8) / (1 - x)^9 + O(x^40)) \\ _Colin Barker_, Jun 19 2018
%Y Cf. A014626, A159359.
%K nonn,easy
%O 2,1
%A _R. H. Hardin_, Apr 11 2009
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