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

0,3

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.

Example

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

Crossrefs

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

Sequence in context: A019213 A019128 A296419 * A283433 A121463 A244608

Adjacent sequences: A301387 A301388 A301389 * A301391 A301392 A301393

Keyword

nonn,tabl

Author

R. J. Mathar, Mar 20 2018

Extensions

More terms from Alois P. Heinz, Mar 20 2018

Status

approved