A389371 Number of distinct branching structures with up to 3 branches per node after n generations.

1, 2, 4, 15, 576, 31850977, 5385388331425639629954, 26031537804569884381299734265433494980888832735504738666061548740

Offset

0,2

Comments

This sequence models a simplified combinatorial growth of natural branching structures (e.g., trees, corals, or vascular networks). Each branch may split into 0, 1, 2, or 3 new branches at each generation. The sequence grows extremely rapidly due to combinatorial explosion.

Links

Table of n, a(n) for n=0..7.

Formula

a(0) = 1; for n >= 1, a(n) = Sum_{k=0..3} binomial(a(n-1), k)

Mathematica

n = 7; NestList[Total@Binomial[#, Range[0, 3]] &, 1, n]

Crossrefs

Cf. A000108, A006894.

Sequence in context: A264832 A389181 A100528 * A378300 A132483 A153064

Adjacent sequences: A389368 A389369 A389370 * A389372 A389373 A389374

Keyword

nonn

Author

Dirk Broeders, Nov 02 2025

Status

approved