A001024 Powers of 15.

1, 15, 225, 3375, 50625, 759375, 11390625, 170859375, 2562890625, 38443359375, 576650390625, 8649755859375, 129746337890625, 1946195068359375, 29192926025390625, 437893890380859375, 6568408355712890625, 98526125335693359375, 1477891880035400390625, 22168378200531005859375, 332525673007965087890625

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Same as Pisot sequences E(1, 15), L(1, 15), P(1, 15), T(1, 15). Essentially same as Pisot sequences E(15, 225), L(15, 225), P(15, 225), T(15, 225). See A008776 for definitions of Pisot sequences.

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

Number of ways to assign truth values to n quaternary disjunctions connected by conjunctions such that the proposition is true. For example, a(2) = 225, since for the proposition (a v b v c v d) & (e v f v g v h) there are 225 assignments that make the proposition true. - Ori Milstein, Jan 26 2023

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; 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 (15).

Crossrefs

a(n) = A159991(n)/A000302(n). - Reinhard Zumkeller, May 02 2009

Row 6 of A329332.

Programs

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] ];

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 *)

PARI

a(n)=15^n \\ Charles R Greathouse IV, Sep 24 2015

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

Extensions

More terms from James Sellers, Sep 19 2000