A146880 A symmetrical triangle sequence of coefficients : p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[(1 + Mod[Binomial[n, m], 2])*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 6, 8, 6, 1, 1, 9, 12, 12, 9, 1, 1, 8, 19, 22, 19, 8, 1, 1, 11, 25, 39, 39, 25, 11, 1, 1, 10, 30, 58, 72, 58, 30, 10, 1, 1, 13, 38, 86, 128, 128, 86, 38, 13, 1, 1, 12, 49, 122, 212, 254, 212, 122, 49, 12, 1

Offset

0,5

Comments

Row sums are:{1, 2, 6, 16, 22, 44, 78, 152, 270, 532, 1046}.

Links

Table of n, a(n) for n=0..65.

Formula

p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[(1 + Mod[Binomial[n, m], 2])*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; t(n,m)=coefficients(p(x,n)).

Example

{1}, {1, 1}, {1, 4, 1}, {1, 7, 7, 1}, {1, 6, 8, 6, 1}, {1, 9, 12, 12, 9, 1}, {1, 8, 19, 22, 19, 8, 1}, {1, 11, 25, 39, 39, 25, 11, 1}, {1, 10, 30, 58, 72, 58, 30, 10, 1}, {1, 13, 38, 86, 128, 128, 86, 38, 13, 1}, {1, 12, 49, 122, 212, 254, 212, 122, 49, 12, 1}

Mathematica

Clear[p, x, n]; p[x_, n_] = If[ n == 0, 1, (x + 1)^n +Sum[(1 + Mod[Binomial[n, m], 2])*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: A355777 A223489 A016521 * A152236 A296180 A157172

Adjacent sequences: A146877 A146878 A146879 * A146881 A146882 A146883

Keyword

nonn

Author

Roger L. Bagula, Nov 02 2008

Status

approved