A009975 Powers of 31: a(n) = 31^n.

1, 31, 961, 29791, 923521, 28629151, 887503681, 27512614111, 852891037441, 26439622160671, 819628286980801, 25408476896404831, 787662783788549761, 24417546297445042591, 756943935220796320321, 23465261991844685929951, 727423121747185263828481

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Same as Pisot sequences E(1, 31), L(1, 31), P(1, 31), T(1, 31). Essentially same as Pisot sequences E(31, 961), L(31, 961), P(31, 961), T(31, 961). 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 31-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 (31).

Programs

Mathematica

Table[31^n, {n, 0, 15}] (* Robert P. P. McKone, Jan 04 2022 *)

PARI

a(n)=31^n \\ Charles R Greathouse IV, Sep 24 2015

Formula

G.f.: 1/(1-31*x). - Philippe Deléham, Nov 24 2008

E.g.f.: exp(31x). - Geoffrey Critzer, Feb 28 2009

a(n) = 31*a(n-1). - Zerinvary Lajos, Apr 29 2009