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.
1, 1, 4, 1, 10, 70, 1, 20, 316, 3380, 1, 35, 1045, 23259, 344279, 1, 56, 2806, 112976, 3286101, 63241196, 1, 84, 6510, 427440, 21787375, 789333776, 18937075894, 1, 120, 13560, 1347676, 109770025, 6797996276, 296755137820, 8610006123300, 1, 165, 26001, 3702285, 449707069, 43808767121, 3202666462485, 164411906603281, 5637949058244465
Offset: 0
Examples
1 1 4 1 10 70 1 20 316 3380 1 35 1045 23259 344279 1 56 2806 112976 3286101 63241196 1 84 6510 427440 21787375 789333776 18937075894
Links
- Alois P. Heinz, Rows n = 0..10, flattened
Formula
T(n,k) = T(k,n). T(n,0)=1 (the empty matrix).
G.f. column k=2 polynomial is -(1+x)*(6*x^4-18*x^3+19*x^2+2*x+1)/(x-1)^7.
Extensions
More terms from Alois P. Heinz, Mar 20 2018