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A001029
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Powers of 19.
(Formerly M5079 N2198)
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32
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1, 19, 361, 6859, 130321, 2476099, 47045881, 893871739, 16983563041, 322687697779, 6131066257801, 116490258898219, 2213314919066161, 42052983462257059, 799006685782884121, 15181127029874798299, 288441413567621167681, 5480386857784802185939, 104127350297911241532841, 1978419655660313589123979, 37589973457545958193355601
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OFFSET
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0,2
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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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.
Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 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).
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FORMULA
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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
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MAPLE
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A001029:=-1/(-1+19*z); [Conjectured by Simon Plouffe in his 1992 dissertation.]
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MATHEMATICA
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Table[19^n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)
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PROG
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(Sage) [lucas_number1(n, 19, 0) for n in xrange(1, 17)]# Zerinvary Lajos, Apr 29 2009
(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
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CROSSREFS
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Sequence in context: A171293 A045609 A128360 * A057685 A243399 A041686
Adjacent sequences: A001026 A001027 A001028 * A001030 A001031 A001032
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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