A009980 Powers of 36.

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

Offset

0,2

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).

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

Mathematica

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

Prog

(Magma)[36^n: n in [0..20]] // Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=36^n \\ Charles R Greathouse IV, Nov 18 2011

Crossrefs

Cf. A000400.

Sequence in context: A224194 A224011 A300357 * A041613 A255821 A209042

Adjacent sequences: A009977 A009978 A009979 * A009981 A009982 A009983

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved