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 A001026 Powers of 17. (Formerly M5048 N2182) 30
 1, 17, 289, 4913, 83521, 1419857, 24137569, 410338673, 6975757441, 118587876497, 2015993900449, 34271896307633, 582622237229761, 9904578032905937, 168377826559400929, 2862423051509815793, 48661191875666868481, 827240261886336764177, 14063084452067724991009, 239072435685151324847153, 4064231406647572522401601 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Same as Pisot sequences E(1, 17), L(1, 17), P(1, 17), T(1, 17). Essentially same as Pisot sequences E(17, 289), L(17, 289), P(17, 289), T(17, 289). 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 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 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 281 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 (17). FORMULA 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 MAPLE A001026:=-1/(-1+17*z); [Simon Plouffe in his 1992 dissertation.] MATHEMATICA Table[17^n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *) PROG (Sage) [lucas_number1(n, 17, 0) for n in range(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 CROSSREFS Sequence in context: A171291 A128358 A015969 * A178765 A041546 A186000 Adjacent sequences: A001023 A001024 A001025 * A001027 A001028 A001029 KEYWORD nonn,easy AUTHOR N. J. A. Sloane EXTENSIONS More terms from James A. Sellers, Sep 19 2000 STATUS approved

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Last modified December 4 12:33 EST 2023. Contains 367562 sequences. (Running on oeis4.)