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A001026
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Powers of 17.
(Formerly M5048 N2182)
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20
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1, 17, 289, 4913, 83521, 1419857, 24137569, 410338673, 6975757441, 118587876497, 2015993900449, 34271896307633, 582622237229761, 9904578032905937, 168377826559400929, 2862423051509815793, 48661191875666868481, 827240261886336764177, 14063084452067724991009, 239072435685151324847153, 4064231406647572522401601
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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 17-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011
Numbers n such that sigma(17*n) = 17*n + sigma(n). - Jahangeer Kholdi, Nov 23 2013
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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 281
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 (17).
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FORMULA
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G.f.: 1/(1-17x), e.g.f.: exp(17x).
a(n)=17^n ; a(n)=17*a(n-1) n>0, a(0)=1. - Vincenzo Librandi, Nov 21 2010
G.f.: 1 + x*(G(0) - 1)/(x-1) where G(k) = 1 - (4(k+1)^2+1)/(1-x/(x - 1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jan 15 2013
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MAPLE
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A001026:=-1/(-1+17*z); [Simon Plouffe in his 1992 dissertation.]
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MATHEMATICA
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Table[17^n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)
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PROG
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(Sage) [lucas_number1(n, 17, 0) for n in xrange(1, 17)] # Zerinvary Lajos, Apr 29 2009
(MAGMA)[17^n: n in [0..100]]; // Vincenzo Librandi, Nov 21 2010
(Maxima) A001026(n):=17^n$
makelist(A001026(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */
(PARI) a(n)=17^n \\ Charles R Greathouse IV, Sep 24 2015
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CROSSREFS
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Sequence in context: A171291 A128358 A015969 * A178765 A041546 A186000
Adjacent sequences: A001023 A001024 A001025 * A001027 A001028 A001029
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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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EXTENSIONS
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More terms from James A. Sellers, Sep 19 2000
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STATUS
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approved
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