A009971 Powers of 27.

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

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

Prog

(Sage) [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

Sequence in context: A171301 A098838 A268015 * A307388 A046240 A042406

Adjacent sequences: A009968 A009969 A009970 * A009972 A009973 A009974

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved