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A131060
3*A007318 - 2*A000012 as infinite lower triangular matrices.
12
1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 10, 16, 10, 1, 1, 13, 28, 28, 13, 1, 1, 16, 43, 58, 43, 16, 1, 1, 19, 61, 103, 103, 61, 19, 1, 1, 22, 82, 166, 208, 166, 82, 22, 1, 1, 25, 106, 250, 376, 376, 250, 106, 25, 1, 1, 28, 133, 358, 628, 754, 628, 358, 133, 28, 1
OFFSET
0,5
COMMENTS
Row sums = A097813: (1, 2, 6, 16, 38, 84, 178, ...).
FORMULA
T(n,k) = 3*binomial(n,k) - 2. - Roger L. Bagula, Aug 20 2008
EXAMPLE
First few rows of the triangle:
1;
1, 1;
1, 4, 1;
1, 7, 7, 1;
1, 10, 16, 10, 1;
1, 13, 28, 28, 13, 1;
1, 16, 43, 58, 43, 16, 1;
...
MAPLE
A131060:= (n, k) -> 3*binomial(n, k)-2; seq(seq(A131060(n, k), k = 0..n), n = 0.. 10); # G. C. Greubel, Mar 12 2020
MATHEMATICA
T[n_, k_] = 3*Binomial[n, k] -2; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* Roger L. Bagula, Aug 20 2008 *)
PROG
(Magma) [3*Binomial(n, k) -2: k in [0..n], n in [0..10]]; // G. C. Greubel, Mar 12 2020
(Sage) [[3*binomial(n, k) -2 for k in (0..n)] for n in (0..10)] # G. C. Greubel, Mar 12 2020
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jun 13 2007
EXTENSIONS
More terms from Roger L. Bagula, Aug 20 2008
STATUS
approved