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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.
1
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
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
KEYWORD
nonn,tabl
AUTHOR
R. J. Mathar, Mar 20 2018
EXTENSIONS
More terms from Alois P. Heinz, Mar 20 2018
STATUS
approved