A157896 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A157896

Coefficients of polynomials of a prime like factor set (skip power): p(x,n)=Sum[x^i, {i, 0, (Prime[n] - 1)/2,2}]; q(n,n)=Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2,2}]; t(x,n)=If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]].

1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 3, 3, 2, 2, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,6

COMMENTS

Row sums are:

{1, 2, 8, 32, 50, 128, 200, 242, 392, 512, 648,...}.

LINKS

Table of n, a(n) for n=0..70.

FORMULA

p(x,n)=Sum[x^i, {i, 0, (Prime[n] - 1)/2.2}];

q(n,n)=Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2,2}];

t(x,n)=If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]];

out_(n,m)=coefficients(t(x,n)).

EXAMPLE

{1},

{1, 1},

{1, 1, 2, 2, 1, 1},

{1, 1, 2, 2, 3, 3, 4, 4, 3, 3, 2, 2, 1, 1},

{1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1},

{1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1}

MATHEMATICA

Clear[p, q, t, x, n];

p[x_, n_] := Sum[x^i, {i, 0, (Prime[n] - 1)/2, 2}];

q[x_, n_] := Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2, 2}];

t[x_, n_] := If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]];

Table[ExpandAll[t[x, n]], {n, 0, 10, 2}];

Table[CoefficientList[ExpandAll[t[x, n]], x], {n, 0, 10, 2}];

Flatten[%]

CROSSREFS

Sequence in context: A140193 A073741 A071838 * A358469 A156072 A215788

Adjacent sequences: A157893 A157894 A157895 * A157897 A157898 A157899

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 08 2009

STATUS

approved