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A061377
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a(1) = 1, a(n+1) = numerator of the continued fraction [1; 2, 4, 8, ..., 2^n].
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6
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1, 3, 13, 107, 1725, 55307, 3541373, 453351051, 116061410429, 59423895490699, 60850185043886205, 124621238393774438539, 510448653311085144141949, 4181595492545647894585284747, 68511261060316548415970449436797
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OFFSET
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1,2
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LINKS
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FORMULA
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0 = a(n)*(-2*a(n+2)) + a(n+1)*(+a(n+1) - a(n+3)) + a(n+2)*(+2*a(n+2)) if n>0. - Michael Somos, Dec 28 2016
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EXAMPLE
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G.f. = x + 3*x^2 + 13*x^3 + 107*x^4 + 1725*x^5 + 55307*x^6 + 3541373*x^7 + ...
a(3) = 13, the numerator of 1 + 1/(2 + 1/4) = 13/9.
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MAPLE
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with(numtheory); f := n->numer(cfrac([seq (2^i, i=0..n)])); for n from 0 to 25 do printf("%d, ", f(n)) od;
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MATHEMATICA
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Module[{nn=20, c}, c=2^Range[0, nn]; Table[Numerator[ FromContinuedFraction[ Take[ c, n]]], {n, nn}]] (* Harvey P. Dale, Jun 04 2014 *)
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PROG
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(PARI) {a(n) = if( n<1, 0, n<3, 2*n-1, 2^(n-1)*a(n-1) + a(n-2))}; /* Michael Somos, Dec 28 2016 */
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org) and Winston C. Yang (winston(AT)cs.wisc.edu), May 15 2001
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STATUS
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approved
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