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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A009965 Powers of 21. 22
1, 21, 441, 9261, 194481, 4084101, 85766121, 1801088541, 37822859361, 794280046581, 16679880978201, 350277500542221, 7355827511386641, 154472377739119461, 3243919932521508681, 68122318582951682301, 1430568690241985328321, 30041942495081691894741, 630880792396715529789561, 13248496640331026125580781, 278218429446951548637196401 (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 21-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

LINKS

T. D. Noe, Table of n, a(n) for n = 0..100

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (21).

FORMULA

For A009966-A009992 we have g.f.: 1/(1-qx), e.g.f.: exp(qx), with q = 21, 22, ..., 48. - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 07 2001

a(n)=21^n; a(n)=21*a(n-1) n>0 a(0)=1 [From Vincenzo Librandi, Nov 21 2010]

G.f.: 22/G(0) where G(k) = 1 - 2*x*(k+1)/(1 - 1/(1 - 2*x*(k+1)/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 10 2013.

PROG

(Sage) [lucas_number1(n, 21, 0) for n in xrange(1, 17)]# [From Zerinvary Lajos, Apr 29 2009]

(MAGMA)[21^n: n in [0..100]][From Vincenzo Librandi, Nov 21 2010]

(PARI) a(n)=21^n \\ Charles R Greathouse IV, Nov 18 2011

(Maxima) A009965(n):=21^n$

makelist(A009965(n), n, 0, 30); /* Martin Ettl, Nov 07 2012 */

CROSSREFS

Sequence in context: A224009 A167255 A171295 * A189433 A041842 A215152

Adjacent sequences:  A009962 A009963 A009964 * A009966 A009967 A009968

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

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 April 28 05:37 EDT 2017. Contains 285557 sequences.