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A279543
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a(n) = a(n-1) + 3^n * a(n-2) with a(0) = 1 and a(1) = 1.
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3
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1, 1, 10, 37, 847, 9838, 627301, 22143007, 4137864868, 439978671649, 244776761262181, 78185678507867584, 130162592460442600405, 124783388108159412726037, 622688428086038843429228482, 1791127919536971393223950620041
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OFFSET
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0,3
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COMMENTS
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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).
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..90
Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction
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EXAMPLE
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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).
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MATHEMATICA
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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 *)
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Dec 31 2016
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STATUS
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approved
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