A202150 - OEIS

A202150

a(n) = A202146( 3*n*(n+1) ) for n>=0.

1, 1, 1, -1, 1, -1, 1, 3, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 3, -1, 1, 1, 1, 1, -1, -1, 1, 1, 3, -1, -1, -1, 1, 3, 3, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 3, 1, 1, 1, 1, -1, -1, -1, 3, 3, 1, -1, -1, 1, 1, -1, 1, -1, 3

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OFFSET

0,8

COMMENTS

Conjecture: this sequence consists of all odd terms in A202146; the g.f. of A202146 is 1/(1-x) + Sum_{n>=1} x^n/(1-x) * Product_{k=1..n} (1 - x^k) / (1 - x^(2*k+1)), which by the conjecture has an odd coefficient of x^m iff m = 3*n*(n+1) for n>=0. The conjecture holds for at least the initial 30300 terms of A202146.

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..100

PROG

(PARI) {a(n)=polcoeff((1+sum(m=1, 3*n*(n+1), x^m*prod(k=1, m, (1-x^k)/(1-x^(2*k+1) +x*O(x^(3*n*(n+1)))))))/(1-x+x*O(x^(3*n*(n+1)))), 3*n*(n+1))}

CROSSREFS

Cf. A202146.

Sequence in context: A363329 A370079 A318497 * A093818 A097031 A372565

Adjacent sequences: A202147 A202148 A202149 * A202151 A202152 A202153

KEYWORD

sign

AUTHOR

Paul D. Hanna, Dec 12 2011

STATUS

approved