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%I #9 Sep 03 2018 23:06:43
%S 1,1,4,10,33,78,224,549,1403,3292,7677,16934,36581,75732,152949,
%T 298784,569636,1056500,1916502,3396630,5901524,10051384,16820192,
%U 27664756,44795247,71442327,112366941,174384376,267289440,404838044,606375995
%N Number of nonnegative integer 4 X 4 matrices with sum of elements equal to n, under row and column permutations.
%H Andrew Howroyd, <a href="/A052366/b052366.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: (x^34 - 4*x^33 + 6*x^32 - x^31 + 3*x^30 - 11*x^29 + 33*x^28 - 19*x^27 + 81*x^26 - 52*x^25 + 152*x^24 - 36*x^23 + 255*x^22 - 130*x^21 + 367*x^20 - 84*x^19 + 350*x^18 - 94*x^17 + 350*x^16 - 84*x^15 + 367*x^14 - 130*x^13 + 255*x^12 - 36*x^11 + 152*x^10 - 52*x^9 + 81*x^8 - 19*x^7 + 33*x^6 - 11*x^5 + 3*x^4 - x^3 + 6*x^2 - 4*x + 1)/((x^10 + x^9 - x^7 - x^6 + x^4 + x^3 - x - 1)*(x^6 - 1)^2*(x^2 + 1)^3*(x^2 - 1)^4*(x^2 + x + 1)^2*(x + 1)*(x - 1)^9).
%Y Row 4 of A318795.
%Y Cf. A002724, A053307, A052365.
%K nonn
%O 0,3
%A _Vladeta Jovovic_, Mar 08 2000
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