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Search: id:A128272
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| A128272 |
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a(n) = the numerator of b(n): {b(n)} is such that the continued fraction (of rational terms) [b(1);b(2),...,b(n)] equals the F(n+1)^2/F(n)^2, for every positive integer n, where F(n) is the n-th Fibonacci number. |
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+0
2
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| 1, 1, 15, 77, 5301, 189679, 87596289, 21608003585, 68221625702463, 115452529488363949, 2497495662248930113941, 80258100236324702562311, 4295613290302749695769359713665, 341566880541004135370464340131322497
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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limit{n -> inf} b(n)*b(n+1) = 1.
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EXAMPLE
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b(n): 1, 1/3, 15/7, 77/171, 5301/2401,...
F(5)^2/F(4)^2 = 25/9 equals [b(1);b(2),b(3),b(4)] = 1 +1/(1/3 +1/(15/7 +171/77)).
F(6)^2/F(5)^2 = 64/25 equals [b(1);b(2),b(3),b(4),b(5)] = 1 +1/(1/3 +1/(15/7 +1/(77/171 +2401/5301)).
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MAPLE
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A128272 := proc(nmax) local a, b, i, n, ffrac ; b := [1] ; while nops(b) < nmax do n := nops(b)+1 ; ffrac := (combinat[fibonacci](n+1)/combinat[fibonacci](n))^2 ; for i from 1 to n-1 do ffrac := 1/(ffrac-b[i]) ; od: b := [op(b), ffrac] ; od: a := [] ; for i from 1 to nops(b) do a := [op(a), numer(op(i, b))] ; od: RETURN(a) ; end: op(A128272(14)) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 08 2007
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CROSSREFS
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Cf. A128273.
Sequence in context: A000477 A041430 A051423 this_sequence A081591 A044202 A044583
Adjacent sequences: A128269 A128270 A128271 this_sequence A128273 A128274 A128275
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KEYWORD
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frac,nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Feb 22 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 08 2007
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