A135361 a(n) = a(n-1)^3 + 1 with a(0) = 0.

0, 1, 2, 9, 730, 389017001, 58871587162270593034051002, 204040901322752673844230437877671861543858084850895762746141813554591014612009

Offset: 0

Author

Gerald McGarvey, Dec 08 2007

Keywords

• easy
• nonn

Comments

Number of ternary trees of height less than n.

The rightmost digits cycle (0, 1, 2, 9, 0, 1, 2, 9, ...).

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..9
• Robin Lamarche-Perrin, An Information-theoretic Framework for the Lossy Compression of Link Streams, arXiv:1807.06874 [cs.DS], 2018.
• C. Lenormand, Arbres et permutations, 1.2: Magmas et Arborescences, pp. 55, 57.

Crossrefs

Cf. A003095, A008322, A119731.

Programs

Mathematica

Nest[Append[#, #[[-1]]^3 + 1] &, {0}, 7] (* Michael De Vlieger, Oct 24 2018 *)

Sage

def a(n): return 0 if (n==0) else a(n-1)^3 + 1
[a(n) for n in (0..9)] # G. C. Greubel, Jul 19 2021

Formula

a(n) is asymptotic to c^(3^n) where c=1.0847999710783722816939038440390528005339362697...