A111330 - OEIS

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A111330

Let qf(a,q) = Product_{j >= 0} (1-a*q^j); g.f. is qf(q,q^4)/qf(q^3,q^4).

1, -1, 0, 1, -1, -1, 2, 0, -2, 1, 1, -1, -1, 1, 2, -2, -2, 3, 1, -4, 0, 5, -1, -5, 2, 5, -4, -5, 6, 4, -6, -4, 7, 4, -10, -2, 12, 0, -13, 2, 13, -4, -14, 6, 17, -10, -17, 14, 15, -17, -15, 21, 15, -26, -13, 31, 9, -35, -5, 39, 2, -44, 3, 49, -12, -52, 21, 53, -27, -55, 35, 57, -47, -57, 59, 55, -69, -52, 80, 49, -95, -43, 110, 34, -122

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

OFFSET

0,7

LINKS

Table of n, a(n) for n=0..84.

FORMULA

From Peter Bala, Nov 28 2020: (Start)

O.g.f.: A(x) = F(x)/G(x) where F(x) = Product_{k >= 0} 1 - x^(4*k+1) (see A284313) and G(x) = Product_{k >= 0} 1 - x^(4*k+3) (see A284316).

Continued fraction representations: A(x) = 1 - x/(1 + x^2 - x^3/(1 + x^4 - x^5/(1 + x^6 - ... ))).

A(x) = 1 - x/(1 - x^2*(x - 1)/(1 - x^5/(1 - x^4*(x^3 - 1)/(1 - x^9/(1 - x^6*(x^5 - 1)/(1 - ... )))))). Cf. A224704. (End)

CROSSREFS

Cf. A111317, A111335, A111374, A224704, A284313, A284316.