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

Author

Jakub Zaborowski, Nov 20 2019

Keywords

• nonn

Links

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

Crossrefs

Cf. A000002, A054352, A054353.

Programs

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

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

Extensions

More terms from Jack W Grahl, May 04 2020