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A301390 The number of n X k matrices, k=0..n, with nonnegative integer entries and every row and column sum <=3 . Triangle T(n>=0, 0<=k<=n) read by rows.

%I A301390 #19 Mar 21 2018 13:45:02
%S A301390 1,1,4,1,10,70,1,20,316,3380,1,35,1045,23259,344279,1,56,2806,112976,
%T A301390 3286101,63241196,1,84,6510,427440,21787375,789333776,18937075894,1,
%U A301390 120,13560,1347676,109770025,6797996276,296755137820,8610006123300,1,165,26001,3702285,449707069,43808767121,3202666462485,164411906603281,5637949058244465
%N A301390 The number of n X k matrices, k=0..n, with nonnegative integer entries and every row and column sum <=3 . Triangle T(n>=0, 0<=k<=n) read by rows.
%H A301390 Alois P. Heinz, <a href="/A301390/b301390.txt">Rows n = 0..10, flattened</a>
%F A301390 T(n,k) = T(k,n). T(n,0)=1 (the empty matrix).
%F A301390 G.f. column k=2 polynomial is -(1+x)*(6*x^4-18*x^3+19*x^2+2*x+1)/(x-1)^7.
%e A301390 1
%e A301390 1  4
%e A301390 1 10   70
%e A301390 1 20  316   3380
%e A301390 1 35 1045  23259   344279
%e A301390 1 56 2806 112976  3286101  63241196
%e A301390 1 84 6510 427440 21787375 789333776 18937075894
%Y A301390 Cf. A131235 (sums <= 2), A086885 (sums <= 1), A000292 (row-column 1).
%K A301390 nonn,tabl
%O A301390 0,3
%A A301390 _R. J. Mathar_, Mar 20 2018
%E A301390 More terms from _Alois P. Heinz_, Mar 20 2018