A009974 Powers of 30.

1, 30, 900, 27000, 810000, 24300000, 729000000, 21870000000, 656100000000, 19683000000000, 590490000000000, 17714700000000000, 531441000000000000, 15943230000000000000, 478296900000000000000, 14348907000000000000000

Offset

0,2

Comments

Same as Pisot sequences E(1, 30), L(1, 30), P(1, 30), T(1, 30). Essentially same as Pisot sequences E(30, 900), L(30, 900), P(30, 900), T(30, 900). 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 30-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 (30).

Formula

G.f.: 1/(1-30*x). - Philippe Deléham, Nov 24 2008

a(n) = 30^n; a(n) = 30*a(n-1), n > 0; a(0)=1. - Vincenzo Librandi, Nov 21 2010

Mathematica

NestList[30#&, 1, 20] (* Harvey P. Dale, Jul 21 2023 *)

Prog

(Sage) [lucas_number1(n, 30, 0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009
(Magma)[30^n: n in [0..100]] // Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=30^n \\ Charles R Greathouse IV, Jun 19 2015
(PARI) powers(30, 12) \\ Charles R Greathouse IV, Jun 19 2015

Crossrefs

Row 7 of A329332.

Sequence in context: A056379 A320670 A171304 * A041421 A042742 A144350

Adjacent sequences: A009971 A009972 A009973 * A009975 A009976 A009977

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved