A123964 Triangle, T(n, k) = k^6 - n^6 - 5*(n*k)^2*(n^2 - k^2) + 4*n*k*((n*k)^4 - 1), read by rows.

0, -1, 0, -64, -3, 4080, -729, -128, 29515, 236160, -4096, -1215, 123168, 986873, 4194240, -15625, -6144, 373899, 3004544, 12770391, 39062400, -46656, -21875, 925648, 7468533, 31750240, 97119349, 241864560, -117649, -62208, 1989555, 16131200, 68598447, 209838336, 522579107, 1129900800

Offset

0,4

Links

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Formula

T(n, k) = k^6 - n^6 - 5*n^2*k^2*(n^2 - k^2) + 4*n*k*(n^4*k^4 - 1).

Example

Triangle begins as:
       0;
      -1,      0;
     -64,     -3,   4080;
    -729,   -128,  29515,  236160;
   -4096,  -1215, 123168,  986873,  4194240;
  -15625,  -6144, 373899, 3004544, 12770391, 39062400;
  -46656, -21875, 925648, 7468533, 31750240, 97119349, 241864560;

Mathematica

T[n_, m_]= m^6 -n^6 - 5*n^2*m^2*(n^2 -m^2) + 4*n*m*(n^4*m^4 -1);
Table[T[n, m], {n, 0, 12}, {m, 0, n}]//Flatten

Prog

(Magma)
A123964:= func< n, k | k^6-n^6 -5*(n*k)^2*(n^2-k^2) +4*n*k*((n*k)^4-1) >;
[A123964(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Aug 20 2023
(SageMath)
def A123964(n, k): return k^6-n^6 -5*(n*k)^2*(n^2-k^2) +4*n*k*((n*k)^4 - 1)
flatten([[A123964(n, k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Aug 20 2023

Crossrefs

Sequence in context: A351246 A371277 A288923 * A298923 A210114 A236179

Adjacent sequences: A123961 A123962 A123963 * A123965 A123966 A123967

Keyword

sign,tabl,easy

Author

Roger L. Bagula, Oct 28 2006

Extensions

Edited by G. C. Greubel, Aug 20 2023

Status

approved