A009989 Powers of 45.

1, 45, 2025, 91125, 4100625, 184528125, 8303765625, 373669453125, 16815125390625, 756680642578125, 34050628916015625, 1532278301220703125, 68952523554931640625, 3102863559971923828125, 139628860198736572265625, 6283298708943145751953125, 282748441902441558837890625

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Same as Pisot sequences E(1, 45), L(1, 45), P(1, 45), T(1, 45). Essentially same as Pisot sequences E(45, 2025), L(45, 2025), P(45, 2025), T(45, 2025). 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 45-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 (45).

Crossrefs

Cf. A000244, A000351, A001019, A001024, A008776.

Programs

Magma

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

Mathematica

45^Range[0,20] (* Harvey P. Dale, May 09 2012 *)

PARI

a(n)=45^n \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: 1/(1-45*x). - Philippe Deléham, Nov 24 2008

a(n) = 45^n; a(n) = 45*a(n-1), a(0)=1. - Vincenzo Librandi, Nov 21 2010

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

E.g.f.: exp(45*x).

a(n) = A000244(n)*A001024(n) = A000351(n)*A001019(n). (End)