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 A285349 Expansion of r(q)^2 / r(q^2) in powers of q where r() is the Rogers-Ramanujan continued fraction. 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 FORMULA a(n) = A138518(n) + A285348(n) for n>0 (conjectured). - Thomas Baruchel, May 14 2018 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. Sequence in context: A156346 A156283 A126123 * A256066 A096832 A016588 Adjacent sequences:  A285346 A285347 A285348 * A285350 A285351 A285352 KEYWORD sign AUTHOR Seiichi Manyama, Apr 17 2017 STATUS approved

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Last modified May 13 19:36 EDT 2021. Contains 343868 sequences. (Running on oeis4.)