A176286 Triangle T(n,k) = 1 + 2*k*(n-k)*(k^2 -n*k +2*n^2) read by rows.
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
Offset: 0
Examples
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;
Links
- G. C. Greubel, Rows n = 0..100 of triangle, flattened
Programs
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GAP
Flat(List([0..12], n-> List([0..n], k-> n^4 -(n-k)^4 -k^4 +1 ))); # G. C. Greubel, Nov 25 2019
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Magma
[n^4 -(n-k)^4 -k^4 +1: k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 25 2019
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Maple
seq(seq(n^4 -(n-k)^4 -k^4 +1, k=0..n), n=0..12); # G. C. Greubel, Nov 25 2019
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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 *) -
PARI
T(n,k) = n^4 -(n-k)^4 -k^4 +1; \\ G. C. Greubel, Nov 25 2019
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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
Formula
T(n,k) = T(n,n-k).
Extensions
Edited by R. J. Mathar, May 03 2013
Comments