0,5

Case k=3,i=2 of Gordon/Goellnitz/Andrews Theorem.

Also number of partitions in which no odd part is repeated, with at most 1 part of size less than or equal to 2 and where differences between parts at distance 2 are greater than 1 when the larger part is odd and greater than 2 when the larger part is even.

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 114.

G. E. Andrews, Three aspects of partitions

Expansion of q^(-1/4)(eta(q^2)*eta(q^3)*eta(q^12))/(eta(q)*eta(q^4)*eta(q^6)) in powers of q. - Michael Somos Jun 28 2004

Euler transform of period 12 sequence [1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, ...]. - Michael Somos Jun 28 2004

Expansion of psi(-q^3) / psi(-q) in powers of q where psi() is a Ramanujan theta function. - Michael Somos Nov 21 2007

Given g.f. A(x), then B(x) = x * A(x^4) satisfies 0=f(B(x), B(x^3)) where f(u, v)= u^3 * (1 + v^4) - v * (1 + u*v)^3. - Michael Somos Nov 21 2007

G.f. is a period 1 Fourier series which satisfies f(-1 / (192 t)) = sqrt(1 / 3) / f(t) where q = exp(2 pi i t). - Michael Somos Nov 21 2007

q + q^5 + q^9 + q^13 + 2*q^17 + 3*q^21 + 3*q^25 + 4*q^29 + 6*q^33 + ...

(PARI) {a(n) = if( n<0, 0, polcoeff( 1 / prod(k=1, n, 1 - ([1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0][(k-1)%12 + 1]) * x^k, 1 + x * O(x^n)), n))} /* Michael Somos Jun 28 2004 */

(PARI) {a(n) = local(A); if( n<0, 0, A = x*O(x^n); polcoeff( (eta(x^2 + A) * eta(x^3 + A) * eta(x^12 + A)) / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A)), n))} /* Michael Somos Jun 28 2004 */

A101195(n)=(-1)^n*a(n).

Sequence in context: A029033 A041003 A067592 this_sequence A101195 A123552 A071610

Adjacent sequences: A036015 A036016 A036017 this_sequence A036019 A036020 A036021

nonn,easy

Olivier Gerard (olivier.gerard(AT)gmail.com)