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

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

Offset

0,3

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.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A003095, A008322, A119731.

Sequence in context: A249903 A008322 A178391 * A023366 A000284 A208219

Adjacent sequences: A135358 A135359 A135360 * A135362 A135363 A135364

Keyword

easy,nonn

Author

Gerald McGarvey, Dec 08 2007

Status

approved