A001029 Powers of 19. (Formerly M5079 N2198)

1, 19, 361, 6859, 130321, 2476099, 47045881, 893871739, 16983563041, 322687697779, 6131066257801, 116490258898219, 2213314919066161, 42052983462257059, 799006685782884121, 15181127029874798299, 288441413567621167681, 5480386857784802185939, 104127350297911241532841, 1978419655660313589123979, 37589973457545958193355601

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

Sequence in context: A171293 A045609 A128360 * A057685 A243399 A041686

Adjacent sequences: A001026 A001027 A001028 * A001030 A001031 A001032

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved