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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.
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%I #19 Mar 21 2018 13:45:02

%S 1,1,4,1,10,70,1,20,316,3380,1,35,1045,23259,344279,1,56,2806,112976,

%T 3286101,63241196,1,84,6510,427440,21787375,789333776,18937075894,1,

%U 120,13560,1347676,109770025,6797996276,296755137820,8610006123300,1,165,26001,3702285,449707069,43808767121,3202666462485,164411906603281,5637949058244465

%N 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 Alois P. Heinz, <a href="/A301390/b301390.txt">Rows n = 0..10, flattened</a>

%F T(n,k) = T(k,n). T(n,0)=1 (the empty matrix).

%F 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 1

%e 1 4

%e 1 10 70

%e 1 20 316 3380

%e 1 35 1045 23259 344279

%e 1 56 2806 112976 3286101 63241196

%e 1 84 6510 427440 21787375 789333776 18937075894

%Y Cf. A131235 (sums <= 2), A086885 (sums <= 1), A000292 (row-column 1).

%K nonn,tabl

%O 0,3

%A _R. J. Mathar_, Mar 20 2018

%E More terms from _Alois P. Heinz_, Mar 20 2018