A285349 Expansion of r(q)^2 / r(q^2) in powers of q where r() is the Rogers-Ramanujan continued fraction.

1, -2, 4, -4, 2, 2, -8, 12, -12, 6, 8, -24, 36, -36, 16, 20, -62, 92, -88, 40, 46, -144, 208, -196, 88, 102, -308, 440, -412, 180, 208, -624, 884, -816, 356, 404, -1206, 1692, -1552, 672, 760, -2244, 3128, -2852, 1224, 1378, -4048, 5612, -5084, 2174, 2428, -7104, 9796, -8836, 3760

Offset: 0

Author

Seiichi Manyama, Apr 17 2017

Keywords

• sign

Comments

Let k(q) = r(q) * r(q^2)^2.

G.f. satisfies: A(q) = (1 - k(q))/(1 + k(q)).

And r(q)^5 = k(q) * A(q)^2.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Wikipedia, Rogers-Ramanujan continued fraction

Crossrefs

r(q)^k / r(q^k): this sequence (k=2), A285628 (k=3), A285629 (k=4), A285630 (k=5).

Cf. A007325, A078905 (r(q)^5), A112274 (k(q)), A285348.

Formula

a(n) = A138518(n) + A285348(n) for n>0 (conjectured). - Thomas Baruchel, May 14 2018