A001026 Powers of 17. (Formerly M5048 N2182)

1, 17, 289, 4913, 83521, 1419857, 24137569, 410338673, 6975757441, 118587876497, 2015993900449, 34271896307633, 582622237229761, 9904578032905937, 168377826559400929, 2862423051509815793, 48661191875666868481, 827240261886336764177, 14063084452067724991009, 239072435685151324847153, 4064231406647572522401601

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 * A368115 A178765 A041546

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