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%I #17 Oct 10 2022 07:55:39
%S 1,1,1,3,6,6,11,26,48,82,201,379,836,1554,3197,6420,12639,25298,50675,
%T 101675,203379,405946,811519,1622692,3249540,6494117,12998399,25991681
%N 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.
%C This sequence is the number of terms in the n-th row of irregular array A138742.
%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A138742%2B3%2B4.py">A138742+3+4.py</a>
%e {r_n}: 1, 1, 2, 5/3, 31/18, 1231/720,...
%e 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.
%Y Cf. A138742, A138744.
%K nonn,more
%O 1,4
%A _Leroy Quet_, Mar 27 2008
%E a(7)-a(28) from _Lucas A. Brown_, Apr 12 2021