A146771 Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n-2)*Sum[Binomial[n-m, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 16, 14, 16, 1, 1, 37, 34, 34, 37, 1, 1, 86, 111, 52, 111, 86, 1, 1, 199, 341, 163, 163, 341, 199, 1, 1, 456, 988, 696, 198, 696, 988, 456, 1, 1, 1033, 2724, 2644, 766, 766, 2644, 2724, 1033, 1, 1, 2314, 7213, 9080, 4050, 764, 4050, 9080

Offset

0,5

Comments

Row sums are: {1, 2, 6, 16, 48, 144, 448, 1408, 4480, 14336, 46080}.

Links

Table of n, a(n) for n=0..62.

Example

Triangle begins:
{1},
{1, 1},
{1, 4, 1},
{1, 7, 7, 1},
{1, 16, 14, 16, 1},
{1, 37, 34, 34, 37, 1},
{1, 86, 111, 52, 111, 86, 1},
{1, 199, 341, 163, 163, 341, 199, 1},
{1, 456, 988, 696, 198, 696, 988, 456, 1},
{1, 1033, 2724, 2644, 766, 766, 2644, 2724, 1033, 1},
{1, 2314, 7213, 9080, 4050, 764, 4050, 9080, 7213, 2314, 1}

Mathematica

p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n-2)*Sum[Binomial[n-m, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]];
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%]

Crossrefs

Sequence in context: A316620 A304676 A316123 * A073697 A209414 A193636

Adjacent sequences: A146768 A146769 A146770 * A146772 A146773 A146774

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Nov 02 2008

Status

approved