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A009989 Powers of 45. 4
1, 45, 2025, 91125, 4100625, 184528125, 8303765625, 373669453125, 16815125390625, 756680642578125, 34050628916015625, 1532278301220703125, 68952523554931640625, 3102863559971923828125, 139628860198736572265625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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 [From Vincenzo Librandi, Nov 21 2010]

MATHEMATICA

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

PROG

(MAGMA)[45^n: n in [0..20]] [From Vincenzo Librandi, Nov 21 2010]

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

CROSSREFS

Sequence in context: A218747 A121009 A264061 * A095658 A279439 A251443

Adjacent sequences:  A009986 A009987 A009988 * A009990 A009991 A009992

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified June 28 05:58 EDT 2017. Contains 288813 sequences.