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%I #6 Jul 04 2012 08:11:52
%S 18,169,880,3249,9522,23753,52544,106009,198770,351233,590832,953625,
%T 1485778,2245489,3304704,4751377,6691410,9251257,12580080,16852705,
%U 22271986,29072121,37521216,47924969,60629426,76025041,94549616
%N Number of 4X4 0..n symmetric arrays with all rows summing to 2*n
%C Row 4 of A213800
%H R. H. Hardin, <a href="/A213802/b213802.txt">Table of n, a(n) for n = 1..173</a>
%F Empirical: a(n) = 4*a(n-1) -3*a(n-2) -8*a(n-3) +14*a(n-4) -14*a(n-6) +8*a(n-7) +3*a(n-8) -4*a(n-9) +a(n-10).
%F Empirical: G.f. -x*(18+97*x+258*x^2+380*x^3+266*x^4+86*x^5+22*x^6+4*x^7-4*x^8+x^9) / ( (1+x)^3*(x-1)^7 ). - _R. J. Mathar_, Jul 04 2012
%e Some solutions for n=4
%e ..2..3..2..1....3..1..1..3....0..1..3..4....2..4..0..2....1..3..1..3
%e ..3..2..0..3....1..4..1..2....1..0..4..3....4..2..2..0....3..4..0..1
%e ..2..0..3..3....1..1..3..3....3..4..1..0....0..2..3..3....1..0..3..4
%e ..1..3..3..1....3..2..3..0....4..3..0..1....2..0..3..3....3..1..4..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Jun 20 2012
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