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A009981 Powers of 37. 9
1, 37, 1369, 50653, 1874161, 69343957, 2565726409, 94931877133, 3512479453921, 129961739795077, 4808584372417849, 177917621779460413, 6582952005840035281, 243569224216081305397, 9012061295995008299689 (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 37-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

Numbers n such that sigma(37*n) = 37*n + sigma(n). - Jahangeer Kholdi, Nov 23 2013

REFERENCES

C. W. Trigg, The Powers of 37, Journal of Recreational Mathematics, Vol. 12:3 (1979-80), 186-191.

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 (37).

FORMULA

G.f.: 1/(1-37*x). - Philippe Deléham, Nov 24 2008

a(n)=37^n; a(n)=37*a(n-1) n>0 a(0)=1. - Vincenzo Librandi, Nov 21 2010

PROG

(MAGMA)[37^n: n in [0..20]]; // Vincenzo Librandi, Nov 21 2010

(PARI) a(n)=37^n \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Sequence in context: A188771 A207185 A189061 * A097315 A158741 A094490

Adjacent sequences:  A009978 A009979 A009980 * A009982 A009983 A009984

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Reference added by William Rex Marshall, Nov 13 2010

STATUS

approved

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Last modified April 25 23:17 EDT 2017. Contains 285426 sequences.