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A001024 Powers of 15.
(Formerly M4990 N2147)
28
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 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 (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 xrange(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

Sequence in context: A189774 A189156 A267731 * A012643 A067222 A154597

Adjacent sequences:  A001021 A001022 A001023 * A001025 A001026 A001027

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 July 25 14:33 EDT 2017. Contains 289795 sequences.