A157633 Triangle T(n,m) read rows: 1 in column m=0 and on the diagonal, 2*m*(n-m)*(m^2-n*m+2*n^2) otherwise.

1, 1, 1, 1, 14, 1, 1, 64, 64, 1, 1, 174, 224, 174, 1, 1, 368, 528, 528, 368, 1, 1, 670, 1024, 1134, 1024, 670, 1, 1, 1104, 1760, 2064, 2064, 1760, 1104, 1, 1, 1694, 2784, 3390, 3584, 3390, 2784, 1694, 1, 1, 2464, 4144, 5184, 5680, 5680, 5184, 4144, 2464, 1, 1

Offset: 0

Author

Roger L. Bagula, Mar 03 2009

Keywords

• nonn
• tabl

Comments

Row sums are (30+9*n^5-10*n^3+n)/15, n>0.

Examples

			{1},
{1, 1},
{1, 14, 1},
{1, 64, 64, 1},
{1, 174, 224, 174, 1},
{1, 368, 528, 528, 368, 1},
{1, 670, 1024, 1134, 1024, 670, 1},
{1, 1104, 1760, 2064, 2064, 1760, 1104, 1},
{1, 1694, 2784, 3390, 3584, 3390, 2784, 1694, 1},
{1, 2464, 4144, 5184, 5680, 5680, 5184, 4144, 2464, 1},
{1, 3438, 5888, 7518, 8448, 8750, 8448, 7518, 5888, 3438, 1}
		

Crossrefs

Cf. A157278

Programs

Mathematica

t[n_, m_] = If[n*m*(n - m) == 0, 1, n^4 - (m^4 + (n - m)^4)];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Formula

T(n,m)= 1 if m=0 or m=n, else n^4 - m^4 - (n - m)^4.

Extensions

Edited by the Associate Editors of the OEIS, Apr 22 2009