A157632 Triangle T(n,m) read by rows: 1 in column m=0 and on the diagonal, else 3*n*m*(n-m).
1, 1, 1, 1, 6, 1, 1, 18, 18, 1, 1, 36, 48, 36, 1, 1, 60, 90, 90, 60, 1, 1, 90, 144, 162, 144, 90, 1, 1, 126, 210, 252, 252, 210, 126, 1, 1, 168, 288, 360, 384, 360, 288, 168, 1, 1, 216, 378, 486, 540, 540, 486, 378, 216, 1, 1, 270, 480, 630, 720, 750, 720, 630, 480, 270, 1
Offset: 0
Examples
{1},
{1, 1},
{1, 6, 1},
{1, 18, 18, 1},
{1, 36, 48, 36, 1},
{1, 60, 90, 90, 60, 1},
{1, 90, 144, 162, 144, 90, 1},
{1, 126, 210, 252, 252, 210, 126, 1},
{1, 168, 288, 360, 384, 360, 288, 168, 1},
{1, 216, 378, 486, 540, 540, 486, 378, 216, 1},
{1, 270, 480, 630, 720, 750, 720, 630, 480, 270, 1}
Crossrefs
Programs
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Mathematica
t[n_, m_] = If[n*m*(n - m) == 0, 1, n^3 - (m^3 + (n - m)^3)]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
Formula
T(n,m)= 1 if m=0 or n=m, else n^3-m^3-(n - m)^3 = 3*n*m*(n-m) =3*A157635(n,m).
Row sums: 2+A083374(n), n>0. - R. J. Mathar, Apr 10 2009
Extensions
Edited by the Associate Editors of the OEIS, Apr 10 2009
Comments