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.

1, 1, 2, 3, 4, 7, 10, 15, 22, 34, 51, 76, 114, 171, 257, 385, 575, 862, 1295, 1941, 2916, 4374, 6558, 9840, 14766, 22151, 33236, 49864, 74775, 112144, 168198, 252313, 378489, 567747, 851649, 1277446, 1916182, 2874172, 4311325, 6466984, 9700248, 14550387, 21825590

Offset

1,3

Links

A.H.M. Smeets, Table of n, a(n) for n = 1..62

Formula

a(n) = A054353(a(1) + ... + a(n-1)) - A054353(a(1) + ... + a(n-2)) for n > 2.

a(n) = A054352(n-1) - A054352(n-2). - A.H.M. Smeets, Apr 08 2024

Prog

(Python)
def A329758():
   x = 1
   g = A000002()
   while True:
       yield x
       acc = 0
       for i in range(0, x):
           acc = acc + next(g)
       x = acc # Jack W Grahl, May 04 2020

Crossrefs

Cf. A000002, A054352, A054353.

Sequence in context: A078159 A129490 A018132 * A100638 A319437 A270659

Adjacent sequences: A329755 A329756 A329757 * A329759 A329760 A329761

Keyword

nonn

Author

Jakub Zaborowski, Nov 20 2019

Extensions

More terms from Jack W Grahl, May 04 2020

Status

approved