A009989 Powers of 45.

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

Offset

0,2

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).

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)

Mathematica

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

Prog

(Magma)[45^n: n in [0..20]]; // Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=45^n \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

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

Sequence in context: A218747 A121009 A264061 * A095658 A381918 A342405

Adjacent sequences: A009986 A009987 A009988 * A009990 A009991 A009992

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved