A138743 Let r_1 = 1. Let r_{m+1} = r_1 + 1/(r_2 + 1/(r_3 +...(r_{m-1} + 1/r_m)...)), a continued fraction of rational terms. Then a(n) is the number of (positive integer) terms in the simple continued fraction of r_n.

1, 1, 1, 3, 6, 6, 11, 26, 48, 82, 201, 379, 836, 1554, 3197, 6420, 12639, 25298, 50675, 101675, 203379, 405946, 811519, 1622692, 3249540, 6494117, 12998399, 25991681

Offset

1,4

Comments

This sequence is the number of terms in the n-th row of irregular array A138742.

Links

Table of n, a(n) for n=1..28.

Lucas A. Brown, A138742+3+4.py

Example

{r_n}: 1, 1, 2, 5/3, 31/18, 1231/720,...
r_5 = 31/18, for instance, equals the simple continued fraction 1+ 1/(1 + 1/(2 + 1/(1 + 1/(1 +1/2)))). There are six integer terms (1,1,2,1,1,2) in this continued fraction, so a(5) = 6.

Crossrefs

Cf. A138742, A138744.

Sequence in context: A378120 A201155 A200534 * A184284 A287882 A066297

Adjacent sequences: A138740 A138741 A138742 * A138744 A138745 A138746

Keyword

nonn,more

Author

Leroy Quet, Mar 27 2008

Extensions

a(7)-a(28) from Lucas A. Brown, Apr 12 2021

Status

approved