OFFSET
0,2
COMMENTS
Same as Pisot sequences E(1, 19), L(1, 19), P(1, 19), T(1, 19). Essentially same as Pisot sequences E(19, 361), L(19, 361), P(19, 361), T(19, 361). 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 19-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 0..100
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 283
Tanya Khovanova, Recursive Sequences
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Index entries for linear recurrences with constant coefficients, signature (19).
FORMULA
G.f.: 1/(1-19x), e.g.f.: exp(19x)
a(n) = 19^n; a(n) = 19*a(n-1) with a(0)=1. - Vincenzo Librandi, Nov 21 2010
MAPLE
A001029:=-1/(-1+19*z); # conjectured by Simon Plouffe in his 1992 dissertation
MATHEMATICA
Table[19^n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)
PROG
(Magma) [ 19^n: n in [0..20] ]; // Vincenzo Librandi, Nov 21 2010
(Magma) [ n eq 1 select 1 else 19*Self(n-1): n in [1..21] ];
(PARI) a(n)=19^n \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved