The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A001022 Powers of 13. (Formerly M4914 N2107) 66
 1, 13, 169, 2197, 28561, 371293, 4826809, 62748517, 815730721, 10604499373, 137858491849, 1792160394037, 23298085122481, 302875106592253, 3937376385699289, 51185893014090757, 665416609183179841, 8650415919381337933, 112455406951957393129, 1461920290375446110677, 19004963774880799438801 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Same as Pisot sequences E(1, 13), L(1, 13), P(1, 13), T(1, 13). Essentially same as Pisot sequences E(13, 169), L(13, 169), P(13, 169), T(13, 169). 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 13-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011 Numbers n such that sigma(13*n) = 13*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 277 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, 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 (13). FORMULA G.f.: 1/(1-13*x). E.g.f.: exp(13*x). a(n) = 13^n. - Vincenzo Librandi, Nov 21 2010 a(n) = 13*a(n-1) n > 0, a(0)=1. - Vincenzo Librandi, Nov 21 2010 a(n) = Sum_{k=0..n} A001021(k)*binomial(n,k). It is well known that Sum_{k=0..n} (h-1)^k*binomial(n,k) = h^n. - Bruno Berselli, Aug 06 2013 EXAMPLE For the fifth formula: a(7) = 1*1 + 12*7 + 144*21 + 1728*35 + 20736*35 + 248832*21 + 2985984*7 + 35831808*1 = 62748517. - Bruno Berselli, Aug 06 2013 MAPLE A001022:=-1/(-1+13*z); # Simon Plouffe in his 1992 dissertation MATHEMATICA Table[13^n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *) PROG (Magma) [13^n: n in [0..100]]; // Vincenzo Librandi, Nov 21 2010 (Maxima) A001022(n):=13^n\$ makelist(A001022(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */ (PARI) first(n)=powers(13, n) \\ Charles R Greathouse IV, Jun 17 2021 CROSSREFS Cf. A001021. Sequence in context: A045593 A045597 A045600 * A195945 A228389 A020533 Adjacent sequences: A001019 A001020 A001021 * A001023 A001024 A001025 KEYWORD nonn,easy AUTHOR N. J. A. Sloane EXTENSIONS More terms from James A. Sellers, Sep 19 2000 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 3 20:15 EST 2024. Contains 370512 sequences. (Running on oeis4.)