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A009986 Powers of 42. 3
1, 42, 1764, 74088, 3111696, 130691232, 5489031744, 230539333248, 9682651996416, 406671383849472, 17080198121677824, 717368321110468608, 30129469486639681536, 1265437718438866624512, 53148384174432398229504 (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 42-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 (42).

FORMULA

G.f.: 1/(1-42*x). [From Philippe Deléham, Nov 24 2008]

a(n)=42^n; a(n)=42*a(n-1) a(0)=1 [From Vincenzo Librandi, Nov 21 2010]

PROG

(MAGMA)[42^n: n in [0..20]] [From Vincenzo Librandi, Nov 21 2010]

CROSSREFS

Sequence in context: A208368 A207716 A208077 * A041841 A236270 A216703

Adjacent sequences:  A009983 A009984 A009985 * A009987 A009988 A009989

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified July 22 12:02 EDT 2017. Contains 289669 sequences.