A113280 A symmetrical triangle of coefficients: t(n,m)=(n - m)*(n - m + 2)*m*(m + 2) + 1.

1, 1, 1, 1, 10, 1, 1, 25, 25, 1, 1, 46, 65, 46, 1, 1, 73, 121, 121, 73, 1, 1, 106, 193, 226, 193, 106, 1, 1, 145, 281, 361, 361, 281, 145, 1, 1, 190, 385, 526, 577, 526, 385, 190, 1, 1, 241, 505, 721, 841, 841, 721, 505, 241, 1, 1, 298, 641, 946, 1153, 1226, 1153, 946

Offset

1,5

Comments

Row sums are:

{1, 2, 12, 52, 159, 390, 826, 1576, 2781, 4618, 7304}.

Links

Table of n, a(n) for n=1..63.

Formula

t(n,m)=(n - m)*(n - m + 2)*m*(m + 2) + 1.

Example

{1},
{1, 1},
{1, 10, 1},
{1, 25, 25, 1},
{1, 46, 65, 46, 1},
{1, 73, 121, 121, 73, 1},
{1, 106, 193, 226, 193, 106, 1},
{1, 145, 281, 361, 361, 281, 145, 1},
{1, 190, 385, 526, 577, 526, 385, 190, 1},
{1, 241, 505, 721, 841, 841, 721, 505, 241, 1},
{1, 298, 641, 946, 1153, 1226, 1153, 946, 641, 298, 1}

Mathematica

Clear[t, n, m] t[n_, m_] = (n - m)*(n - m + 2)*m*(m + 2) + 1; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

Crossrefs

Sequence in context: A146773 A202941 A166341 * A159041 A154979 A146765

Adjacent sequences: A113277 A113278 A113279 * A113281 A113282 A113283

Keyword

nonn,tabl

Author

Roger L. Bagula, Aug 25 2008

Status

approved