A009980 Powers of 36.

1, 36, 1296, 46656, 1679616, 60466176, 2176782336, 78364164096, 2821109907456, 101559956668416, 3656158440062976, 131621703842267136, 4738381338321616896, 170581728179578208256, 6140942214464815497216, 221073919720733357899776, 7958661109946400884391936

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Same as Pisot sequences E(1, 36), L(1, 36), P(1, 36), T(1, 36). Essentially same as Pisot sequences E(36, 1296), L(36, 1296), P(36, 1296), T(36, 1296). See A008776 for definitions of Pisot sequences.

The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n >= 1, a(n) equals the number of 36-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

See David Applegate's comment in A000244 from Feb 20 2017 for a proof of Janjic's assertion. - Alonso del Arte, Sep 03 2017

Links

• T. D. Noe, Table of n, a(n) for n = 0..100
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (36).

Crossrefs

Cf. A000079, A000244, A000400, A001027, A005843, A008776.

Programs

Magma

[36^n: n in [0..20]]; // Vincenzo Librandi, Nov 21 2010

Mathematica

36^Range[0, 20]  (* Harvey P. Dale, Mar 04 2011 *)

PARI

a(n)=36^n \\ Charles R Greathouse IV, Nov 18 2011

Formula

G.f.: 1/(1-36*x). - Philippe Deléham, Nov 24 2008

a(n) = 36^n; a(n) = 36*a(n-1) for n > 0, a(0) = 1. - Vincenzo Librandi, Nov 21 2010

From Elmo R. Oliveira, Jul 10 2025: (Start)

E.g.f.: exp(36*x).

a(n) = A000079(n)*A001027(n) = A000400(A005843(n)). (End)