A009984 Powers of 40.

1, 40, 1600, 64000, 2560000, 102400000, 4096000000, 163840000000, 6553600000000, 262144000000000, 10485760000000000, 419430400000000000, 16777216000000000000, 671088640000000000000, 26843545600000000000000

Offset

0,2

Comments

Same as Pisot sequences E(1, 40), L(1, 40), P(1, 40), T(1, 40). Essentially same as Pisot sequences E(40, 1600), L(40, 1600), P(40, 1600), T(40, 1600). 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 40-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 (40).

Formula

G.f.: 1/(1 - 40*x). - Philippe Deléham, Nov 24 2008

a(n) = 40^n; a(n) = 40*a(n-1) a(0) = 1. - Vincenzo Librandi, Nov 21 2010

Mathematica

40^Range[0, 19] (* Alonso del Arte, Sep 04 2016 *)

Prog

(Magma) [40^n: n in [0..20]] // Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=40^n \\ Charles R Greathouse IV, Jun 19 2015
(PARI) powers(40, 10) \\ Charles R Greathouse IV, Jun 19 2015

Crossrefs

Cf. A000302 (powers of 4), A011557 (powers of 10).

Sequence in context: A207425 A207740 A208082 * A041761 A229635 A278431

Adjacent sequences: A009981 A009982 A009983 * A009985 A009986 A009987

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 11 1996

Status

approved