A058082 a(1) = 1; a(n+1) = sum of terms in continued fraction for the sum of the continued fractions, [a(1); a(2), a(3), ..., a(n)] and [0; a(1), a(2), a(3), ..., a(n)].

1, 2, 8, 18, 55, 84, 127, 146, 179, 224, 297, 548, 684, 960, 1627, 1669, 1144, 9307, 20650, 2234, 3977, 2311, 2393, 2523, 4949, 2856, 3118, 11000, 3324, 3230, 3084, 3555, 4173, 3936, 7738, 3786, 4472, 4491, 5188, 4100, 4849, 4674, 6089, 4955, 5862

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

[a(1); a(2)] + [0; a(1), a(2)] = 13/6 = [2; 6]. So a(3) = 2 + 6 = 8.

Maple

A[1]:= 1: v:= 1: P:= <<1, 0>|<0, 1>>:
for n from 2 to 100 do
  P:= P . <<v, 1>|<1, 0>>;
  t:= P[1, 1]/P[2, 1];
  v:=convert(numtheory:-cfrac(t+1/t, `quotients`), `+`);
  A[n]:= v;
od:
seq(A[i], i=1..100); # Robert Israel, Sep 03 2018

Crossrefs

Sequence in context: A119853 A136201 A358907 * A005675 A054358 A268658

Adjacent sequences: A058079 A058080 A058081 * A058083 A058084 A058085

Keyword

nonn

Author

Leroy Quet, Nov 24 2000

Status

approved