OFFSET
0,3
COMMENTS
The Rogers-Ramanujan continued fraction is defined by R(q) = q^(1/5)/(1+q/(1+q^2/(1+q^3/(1+ ... )))). The limit of a(n)/A015459(n+2) is 2^(-1/5) * R(2).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..114
Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction
EXAMPLE
MATHEMATICA
nxt[{n_, a_, b_}]:={n+1, b, b+2^(n+1)*a}; NestList[nxt, {1, 1, 1}, 20][[All, 2]] (* Harvey P. Dale, Jul 17 2020 *)
PROG
(Python)
def a():
a, b, p = 1, 0, 1
while True:
p, a, b = p + p, b, b + p * a
yield b
A280294 = a()
print([next(A280294) for _ in range(19)]) # Peter Luschny, Dec 05 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 31 2016
STATUS
approved