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 A001024 Powers of 15. (Formerly M4990 N2147) 33
 1, 15, 225, 3375, 50625, 759375, 11390625, 170859375, 2562890625, 38443359375, 576650390625, 8649755859375, 129746337890625, 1946195068359375, 29192926025390625, 437893890380859375, 6568408355712890625, 98526125335693359375, 1477891880035400390625, 22168378200531005859375, 332525673007965087890625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A000005(a(n)) = A000290(n+1). - Reinhard Zumkeller, Mar 04 2007 If X_1, X_2, ..., X_n is a partition of the set {1,2,...,2*n} into blocks of size 2 then, for n>=1, a(n) is equal to the number of functions f : {1,2,..., 2*n}->{1,2,3,4} such that for fixed y_1,y_2,...,y_n in {1,2,3,4} we have f(X_i)<>{y_i}, (i=1,2,...,n). - Milan Janjic, May 24 2007 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 15-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011 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 279 Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets 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 (15). FORMULA G.f.: 1/(1-15x), e.g.f.: exp(15x) a(n) = 15^n; a(n) = 15*a(n-1) with a(0)=1. - Vincenzo Librandi, Nov 21 2010 MAPLE A001024:=-1/(-1+15*z); [Simon Plouffe in his 1992 dissertation.] MATHEMATICA Table[15^n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *) PROG (Sage) [lucas_number1(n, 15, 0) for n in range(1, 18)] # Zerinvary Lajos, Apr 29 2009 (MAGMA) [ 15^n: n in [0..20] ]; // Vincenzo Librandi, Nov 21 2010 (MAGMA) [ n eq 1 select 1 else 15*Self(n-1): n in [1..21] ]; (PARI) a(n)=15^n \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS a(n) = A159991(n)/A000302(n). - Reinhard Zumkeller, May 02 2009 Row 6 of A329332. Sequence in context: A189774 A189156 A267731 * A012643 A067222 A154597 Adjacent sequences:  A001021 A001022 A001023 * A001025 A001026 A001027 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from James A. Sellers, Sep 19 2000 STATUS approved

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Last modified April 14 05:41 EDT 2021. Contains 342946 sequences. (Running on oeis4.)