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A329758 Number of n-th generation nodes of a rooted binary tree whose m-th node has exactly A000002(m) descendants, where A000002 is the Kolakoski sequence.

%I A329758 #32 Apr 08 2024 21:53:37
%S A329758 1,1,2,3,4,7,10,15,22,34,51,76,114,171,257,385,575,862,1295,1941,2916,
%T A329758 4374,6558,9840,14766,22151,33236,49864,74775,112144,168198,252313,
%U A329758 378489,567747,851649,1277446,1916182,2874172,4311325,6466984,9700248,14550387,21825590
%N A329758 Number of n-th generation nodes of a rooted binary tree whose m-th node has exactly A000002(m) descendants, where A000002 is the Kolakoski sequence.
%H A329758 A.H.M. Smeets, <a href="/A329758/b329758.txt">Table of n, a(n) for n = 1..62</a>
%F A329758 a(n) = A054353(a(1) + ... + a(n-1)) - A054353(a(1) + ... + a(n-2)) for n > 2.
%F A329758 a(n) = A054352(n-1) - A054352(n-2). - _A.H.M. Smeets_, Apr 08 2024
%o A329758 (Python)
%o A329758 def A329758():
%o A329758    x = 1
%o A329758    g = A000002()
%o A329758    while True:
%o A329758        yield x
%o A329758        acc = 0
%o A329758        for i in range(0, x):
%o A329758            acc = acc + next(g)
%o A329758        x = acc # _Jack W Grahl_, May 04 2020
%Y A329758 Cf. A000002, A054352, A054353.
%K A329758 nonn
%O A329758 1,3
%A A329758 _Jakub Zaborowski_, Nov 20 2019
%E A329758 More terms from _Jack W Grahl_, May 04 2020