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A009975 Powers of 31. 39
1, 31, 961, 29791, 923521, 28629151, 887503681, 27512614111, 852891037441, 26439622160671, 819628286980801, 25408476896404831, 787662783788549761, 24417546297445042591, 756943935220796320321, 23465261991844685929951 (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 31-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

Numbers n such that sigma(31*n) = 31*n + sigma(n). - Jahangeer Kholdi, Nov 23 2013

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 (31).

FORMULA

G.f.: 1/(1-31*x). - Philippe Deléham, Nov 24 2008

E.g.f.: exp(31x). - Geoffrey Critzer, Feb 28 2009

a(n) = 31*a(n-1). - Zerinvary Lajos, Apr 29 2009

PROG

(Sage) [lucas_number1(n, 31, 0) for n in xrange(1, 17)]# - Zerinvary Lajos, Apr 29 2009

(PARI) a(n)=31^n \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Sequence in context: A207431 A208373 A171305 * A042862 A159674 A138958

Adjacent sequences:  A009972 A009973 A009974 * A009976 A009977 A009978

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 24 20:14 EDT 2017. Contains 288707 sequences.