OFFSET
0,5
COMMENTS
This could be written T(n,k) = 1 - (n-k)^3 - k^3 + n^3, where squares (instead of cubes) would define A130154.
Row sums are {1, 2, 9, 40, 125, 306, 637, 1184, 2025, 3250, 4961, ...} = (n+1)^2*(n^2 -2*n +2)/2.
LINKS
G. C. Greubel, Rows n = 0..100 of triangle, flattened
FORMULA
T(n,k) = T(n,n-k).
T(n,k) = 1 + 3*n*k*(n-k).
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 7, 1;
1, 19, 19, 1;
1, 37, 49, 37, 1;
1, 61, 91, 91, 61, 1;
1, 91, 145, 163, 145, 91, 1;
1, 127, 211, 253, 253, 211, 127, 1;
1, 169, 289, 361, 385, 361, 289, 169, 1;
1, 217, 379, 487, 541, 541, 487, 379, 217, 1;
1, 271, 481, 631, 721, 751, 721, 631, 481, 271, 1;
MAPLE
seq(seq(1 + 3*n*k*(n-k), k=0..n), n=0..12); # G. C. Greubel, Nov 25 2019
MATHEMATICA
Flatten[Table[1+3n k(n-k), {n, 0, 20}, {k, 0, n}]] (* Harvey P. Dale, Jul 03 2013 *)
PROG
(PARI) T(n, k) = 1 + 3*n*k*(n-k); \\ G. C. Greubel, Nov 25 2019
(Magma) [1 + 3*n*k*(n-k): k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 25 2019
(Sage) [[1 + 3*n*k*(n-k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Nov 25 2019
(GAP) Flat(List([0..12], n-> List([0..n], k-> 1 + 3*n*k*(n-k) ))); # G. C. Greubel, Nov 25 2019
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Apr 14 2010
EXTENSIONS
Edited by R. J. Mathar, May 03 2013
STATUS
approved