login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001027 Powers of 18.
(Formerly M5062 N2192)
11
1, 18, 324, 5832, 104976, 1889568, 34012224, 612220032, 11019960576, 198359290368, 3570467226624, 64268410079232, 1156831381426176, 20822964865671168, 374813367582081024, 6746640616477458432, 121439531096594251776, 2185911559738696531968, 39346408075296537575424, 708235345355337676357632, 12748236216396078174437376 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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 18-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 282

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 (18).

FORMULA

G.f.: 1/(1-18x), e.g.f.: exp(18x)

a(n) = 18^n; a(n) = 18*a(n-1) with a(0)=1. - Vincenzo Librandi, Nov 21 2010

MAPLE

A001027:=-1/(-1+18*z); [Simon Plouffe in his 1992 dissertation.]

MATHEMATICA

Table[18^n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)

PROG

(Sage) from sage.combinat.sloane_functions import recur_gen2b; it = recur_gen2b(1, n/3, n/3, 0, lambda n: 0); [it.next() for i in range(18)] # Zerinvary Lajos, Jul 16 2008

(Sage) [lucas_number1(n, 18, 0) for n in xrange(1, 17)] # Zerinvary Lajos, Apr 29 2009

(MAGMA) [ 18^n: n in [0..20] ]; // Vincenzo Librandi, Nov 21 2010

(PARI) a(n)=18^n \\ Charles R Greathouse IV, Sep 28 2015

CROSSREFS

Sequence in context: A207498 A285878 A171292 * A285875 A223311 A041145

Adjacent sequences:  A001024 A001025 A001026 * A001028 A001029 A001030

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 | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 23 06:42 EDT 2017. Contains 286909 sequences.