OFFSET
0,5
COMMENTS
This could be written T(n,k) = 1-(n-k)^4 -k^4 +n^4, the quartic analog of A176284.
Row sums are {1, 2, 17, 132, 577, 1798, 4529, 9864, 19329, 34954, 59345, ...} = (n+1)*(9*n^4 -9*n^3 -n^2 +n +15)/15.
LINKS
G. C. Greubel, Rows n = 0..100 of triangle, flattened
FORMULA
T(n,k) = T(n,n-k).
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 15, 1;
1, 65, 65, 1;
1, 175, 225, 175, 1;
1, 369, 529, 529, 369, 1;
1, 671, 1025, 1135, 1025, 671, 1;
1, 1105, 1761, 2065, 2065, 1761, 1105, 1;
1, 1695, 2785, 3391, 3585, 3391, 2785, 1695, 1;
1, 2465, 4145, 5185, 5681, 5681, 5185, 4145, 2465, 1;
1, 3439, 5889, 7519, 8449, 8751, 8449, 7519, 5889, 3439, 1;
MAPLE
seq(seq(n^4 -(n-k)^4 -k^4 +1, k=0..n), n=0..12); # G. C. Greubel, Nov 25 2019
MATHEMATICA
(* First program *)
f[n_, m_, q_]:= f[n, m, q] = 1 -(n-m)^q -m^q +n^q;
Table[Flatten[Table[Table[f[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}]
(* Second program *)
Table[n^4 -(n-k)^4 -k^4 +1, {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 25 2019 *)
PROG
(PARI) T(n, k) = n^4 -(n-k)^4 -k^4 +1; \\ G. C. Greubel, Nov 25 2019
(Magma) [n^4 -(n-k)^4 -k^4 +1: k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 25 2019
(Sage) [[n^4 -(n-k)^4 -k^4 +1 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-> n^4 -(n-k)^4 -k^4 +1 ))); # 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