A146881 A symmetrical triangle sequence of coefficients : p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[(1 + Mod[Binomial[n, m], 4])*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].

1, 1, 1, 1, 8, 1, 1, 11, 11, 1, 1, 6, 12, 6, 1, 1, 9, 16, 16, 9, 1, 1, 12, 23, 22, 23, 12, 1, 1, 15, 25, 43, 43, 25, 15, 1, 1, 10, 30, 58, 76, 58, 30, 10, 1, 1, 13, 38, 86, 132, 132, 86, 38, 13, 1, 1, 16, 49, 122, 216, 254, 216, 122, 49, 16, 1

Offset

0,5

Comments

Row sums are:{1, 2, 10, 24, 26, 52, 94, 168, 274, 540, 1062}.

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], 4])*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; t(n,m)=coefficients(p(x,n)).

Example

{1}, {1, 1}, {1, 8, 1}, {1, 11, 11, 1}, {1, 6, 12, 6, 1}, {1, 9, 16, 16, 9, 1}, {1, 12, 23, 22, 23, 12, 1}, {1, 15, 25, 43, 43, 25, 15, 1}, {1, 10, 30, 58, 76, 58, 30, 10, 1}, {1, 13, 38, 86, 132, 132, 86, 38, 13, 1}, {1, 16, 49, 122, 216, 254, 216, 122, 49, 16, 1}

Mathematica

Clear[p, x, n]; p[x_, n_] = If[ n == 0, 1, (x + 1)^n +Sum[(1 + Mod[Binomial[n, m], 4])*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: A133823 A168643 A173742 * A174301 A174378 A131067

Adjacent sequences: A146878 A146879 A146880 * A146882 A146883 A146884

Keyword

nonn

Author

Roger L. Bagula, Nov 02 2008

Status

approved