A054657 Number of leaves on the rooted tree of height n constructed by the following rule. Assign weight 1 to the single node at height 1. At each node of weight w at height k>0, branch to nodes at height k+1 as follows: one node of weight 1 and a node of weight d+1 if d divides w.

1, 2, 5, 13, 35, 94, 255, 691, 1876, 5092, 13829, 37553, 101992, 276995, 752307, 2043218, 5549310, 15071694, 40934215, 111175866, 301949926, 820085698, 2227325273, 6049340413, 16429805791, 44622800991, 121194031561, 329158925122, 893984605415, 2428032213452

Offset

1,2

Comments

If the condition "d divides w" in the definition is replaced by "d<=w" then sequence A000108 (the Catalan numbers) is obtained.

Links

Table of n, a(n) for n=1..30.

Sean A. Irvine, Java program (github)

Crossrefs

Sequence in context: A335725 A367656 A240609 * A024576 A057960 A339479

Adjacent sequences: A054654 A054655 A054656 * A054658 A054659 A054660

Keyword

nonn

Author

John W. Layman, Apr 17 2000

Extensions

More terms from Sean A. Irvine, Feb 15 2022

Status

approved