A138744 - OEIS

A138744

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 sum of the (positive integer) terms in the simple continued fraction of r_n.

1, 1, 2, 4, 8, 33, 128, 109, 344, 3760, 1829, 18367, 11168, 35246, 41103, 79356, 151643, 344725, 1249071, 1678788, 5385320, 19780986, 17348076, 30966961, 85647848, 160394455, 451333739, 623813606

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OFFSET

1,3

COMMENTS

This sequence is the sum 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_5 = 31/18, for instance, equals the simple continued fraction 1+ 1/(1 + 1/(2 + 1/(1 + 1/(1 +1/2)))). The integer terms in this continued fraction are (1,1,2,1,1,2); so a(5) = 1+1+2+1+1+2 = 8.

CROSSREFS

Cf. A138742, A138743.

Sequence in context: A191650 A036544 A094334 * A243547 A263623 A070897

Adjacent sequences: A138741 A138742 A138743 * A138745 A138746 A138747

KEYWORD

nonn,more

AUTHOR

Leroy Quet, Mar 27 2008

EXTENSIONS

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

STATUS

approved