OFFSET
0,2
COMMENTS
Same as Pisot sequences E(1, 25), L(1, 25), P(1, 25), T(1, 25). Essentially same as Pisot sequences E(25, 625), L(25, 625), P(25, 625), T(25, 625). 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 25-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 (25).
FORMULA
G.f.: 1/(1-25*x). - Philippe Deléham, Nov 23 2008
E.g.f.: exp(25*x). - Zerinvary Lajos, Apr 29 2009
a(n) = 25^n; a(n) = 25*a(n-1), n > 0; a(0)=1. - Vincenzo Librandi, Nov 21 2010
a(n) = A000351(2n) = 5^(2n). - M. F. Hasler, Sep 02 2021
MATHEMATICA
25^Range[0, 20] (* or *) NestList[25#&, 1, 20] (* Harvey P. Dale, Dec 12 2016 *)
PROG
(Sage) [lucas_number1(n, 25, 0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009
(Magma) [25^n: n in [0..100]] // Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=25^n \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved