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A157895 Coefficients of polynomials of a prime like factor set : p(x,n)=Sum[x^i, {i, 0, (Prime[n] - 1)/2}]; q(n,n)=Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2}]; t(x,n)=If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]]. 0
1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are:

{1, 2, 0, 6, 0, 0, 14, 18, 0, 0, 30, 0, 38, 42, 0, 0, 54, 0, 62, 0, 0,...}.

This row sum minus one picks out as cyclotomic the primes; A002144:

{5,13,17,29,37,41,53,61,...}

LINKS

Table of n, a(n) for n=0..93.

FORMULA

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

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

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

{1, 1, 1, 1, -1, -1, -1, -1},

{1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1},

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

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

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},

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

MATHEMATICA

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

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

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

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

Flatten[%]

CROSSREFS

Sequence in context: A232544 A309873 A162511 * A063747 A077008 A158387

Adjacent sequences: A157892 A157893 A157894 * A157896 A157897 A157898

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Mar 08 2009

STATUS

approved

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Last modified December 5 02:30 EST 2022. Contains 358572 sequences. (Running on oeis4.)