A009984 Powers of 40.

1, 40, 1600, 64000, 2560000, 102400000, 4096000000, 163840000000, 6553600000000, 262144000000000, 10485760000000000, 419430400000000000, 16777216000000000000, 671088640000000000000, 26843545600000000000000, 1073741824000000000000000, 42949672960000000000000000

Offset: 0

Author

N. J. A. Sloane, Dec 11 1996

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000079, A000302, A008776, A009964, A011557, A259076.

Programs

Magma

[40^n: n in [0..20]]; // Vincenzo Librandi, Nov 21 2010

Mathematica

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

PARI

a(n)=40^n \\ Charles R Greathouse IV, Jun 19 2015

PARI

powers(40,10) \\ Charles R Greathouse IV, Jun 19 2015

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

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

E.g.f.: exp(40*x).

a(n) = A000079(n)*A009964(n) = A259076(n)/A000079(n). (End)