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 A279543 a(n) = a(n-1) + 3^n * a(n-2) with a(0) = 1 and a(1) = 1. 3
 1, 1, 10, 37, 847, 9838, 627301, 22143007, 4137864868, 439978671649, 244776761262181, 78185678507867584, 130162592460442600405, 124783388108159412726037, 622688428086038843429228482, 1791127919536971393223950620041 (list; graph; refs; listen; history; text; internal format)
 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)/A015460(n+2) is 3^(-1/5) * R(3). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..90 Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction EXAMPLE 1/1 = a(0)/A015460(2). 1/(1+3/1) = 1/4 = a(1)/A015460(3). 1/(1+3/(1+3^2/1)) = 10/13 = a(2)/A015460(4). 1/(1+3/(1+3^2/(1+3^3/1))) = 37/121 = a(3)/A015460(5). MATHEMATICA RecurrenceTable[{a[n] == a[n - 1] + 3^n*a[n - 2], a[0] == 1, a[1] == 1}, a, {n, 15}] (* Michael De Vlieger, Dec 31 2016 *) CROSSREFS Cf. A015460, A128915. Cf. similar sequences with the recurrence a(n-1) + q^n * a(n-2) for n>1, a(0)=1 and a(1)=1: A280294 (q=2), this sequence (q=3), A280340 (q=10). Sequence in context: A071261 A129426 A215881 * A065009 A031430 A154517 Adjacent sequences: A279540 A279541 A279542 * A279544 A279545 A279546 KEYWORD nonn AUTHOR Seiichi Manyama, Dec 31 2016 STATUS approved

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Last modified March 21 13:27 EDT 2023. Contains 361402 sequences. (Running on oeis4.)