A066356 Numerator of sequence defined by recursion c(n) = 1 + c(n-2) / c(n-1), c(0) = 0, c(1) = 1.
0, 1, 1, 2, 3, 7, 23, 167, 3925, 661271, 2609039723, 1728952269242533, 4516579101127820242349159, 7812958861560974806259705508894834509747, 35298563436210937269618773778802420542715366288238091341051372773
Offset: 0
Programs
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Mathematica
nxt[{a_,b_}]:={b,1+a/b}; NestList[nxt,{0,1},20][[All,1]]//Numerator (* Harvey P. Dale, Sep 26 2016 *) -
PARI
{a(n) = if( n<4, max(0, n) - (n>1), (2 * a(n-1) * a(n-2)^2 - a(n-1)^2 * a(n-4) - a(n-2)^3 * a(n-3)) / (a(n-2) - a(n-3) * a(n-4)))}
Formula
a(n) = (2 * a(n - 1) * a(n - 2)^2 - a(n - 1)^2 * a(n - 4) - a(n - 2)^3 * a(n - 3)) / (a(n - 2) - a(n - 3) * a(n - 4)).
a(n) = b(n) + b(n-1) * a(n-2) where b(n) = A064184(n).
Comments