A009971 Powers of 27.

1, 27, 729, 19683, 531441, 14348907, 387420489, 10460353203, 282429536481, 7625597484987, 205891132094649, 5559060566555523, 150094635296999121, 4052555153018976267, 109418989131512359209, 2954312706550833698643, 79766443076872509863361, 2153693963075557766310747

Offset

0,2

Comments

Same as Pisot sequences E(1, 27), L(1, 27), P(1, 27), T(1, 27). Essentially same as Pisot sequences E(27, 729), L(27, 729), P(27, 729), T(27, 729). 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 27-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

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 (27).

Formula

G.f.: 1/(1-27*x). - Philippe Deléham, Nov 24 2008

a(n) = 27^n; a(n) = 27*a(n-1), n > 0; a(0)=1. - Vincenzo Librandi, Nov 21 2010

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

E.g.f.: exp(27*x).

a(n) = A000244(n)*A001019(n) = A000244(A008585(n)). (End)

Mathematica

27^Range[0, 20] (* Paolo Xausa, Jul 19 2024 *)

Prog

(SageMath) [lucas_number1(n, 27, 0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009
(Magma) [27^n: n in [0..100]]; // Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=27^n \\ Charles R Greathouse IV, Sep 24 2015

Crossrefs

Cf. A000244, A001019, A008585, A008776.

Sequence in context: A171301 A098838 A268015 * A373218 A307388 A046240

Adjacent sequences: A009968 A009969 A009970 * A009972 A009973 A009974

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved