OFFSET
0,3
FORMULA
T(n,k) = n^3 + k^3, n >= 0, 0 <= k <= n.
T(n, k) = A051162(n, k)*(A051162(n, k)^2 + 3* A025581(n, k)^2)/4. See the comment on A051162 for this identity. - Wolfdieter Lang, May 15 2015
G.f. for triangle: -(9*x^5*y^3 - 8*x^4*y^3 - x^4*y^2 + 7*x^3*y^3 - 36*x^3*y^2 - 2*x^2*y^3 + 5*x^3*y + 27*x^2*y^2 + 12*x^2*y - 8*x*y^2 - x^2 + 3*x*y - 4*x - 2*y - 1)*x/((x-1)^4*(x*y-1)^4). - Robert Israel, May 15 2015
EXAMPLE
Triangle begins (modulo 2 plot is a checkerboard):
{0}
{1, 2}
{8, 9, 16}
{27, 28, 35, 54}
{64, 65, 72, 91, 128}
{125, 126, 133, 152, 189, 250}
...
The identity for T(2, 1): 9 = 3*(3^2 + 3*1^2)/4 = 3*12/4 = 9. - Wolfdieter Lang, May 15 2015
MAPLE
seq(seq(n^3+k^3, k=0..n), n=0..10); # Robert Israel, May 15 2015
MATHEMATICA
f[n_, m_, p_] := n^p + m^p p = 3 a = Table[Table[f[n, m, p], {n, 0, m}], {m, 0, 20}] aa = Flatten[a]
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Apr 09 2005
STATUS
approved