OFFSET
0,2
COMMENTS
Same as Pisot sequences E(1, 21), L(1, 21), P(1, 21), T(1, 21). Essentially same as Pisot sequences E(21, 441), L(21, 441), P(21, 441), T(21, 441). See A008776 for definitions of Pisot sequences.
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. - 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
MATHEMATICA
21^Range[0, 20] (* or *) NestList[21#&, 1, 20] (* Harvey P. Dale, Aug 31 2023 *)
PROG
(Sage) [lucas_number1(n, 21, 0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009
(Magma) [21^n: n in [0..100]] // 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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved