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)/A015468(n+2) is 10^(-1/5) * R(10).
a(n) has A004652(n+1) digits. The last n digits are the same as the last n digits of a(n-1). - Robert Israel, Jan 12 2017
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..62
Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction
FORMULA
a(n) a(n-3) = 10 a(n-2) a(n-1) - 10 a(n-2)^2 + a(n-1) a(n-3). - Robert Israel, Jan 12 2017
EXAMPLE
MAPLE
A[0]:= 1: A[1]:= 1:
for n from 2 to 20 do A[n]:= A[n-1]+10^n*A[n-2] od:
seq(A[i], i=0..20); # Robert Israel, Jan 12 2017
MATHEMATICA
RecurrenceTable[{a[0]==a[1]==1, a[n]==a[n-1]+10^n a[n-2]}, a, {n, 15}] (* Harvey P. Dale, Jul 12 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 31 2016
STATUS
approved