A009966 Powers of 22.

1, 22, 484, 10648, 234256, 5153632, 113379904, 2494357888, 54875873536, 1207269217792, 26559922791424, 584318301411328, 12855002631049216, 282810057883082752, 6221821273427820544, 136880068015412051968, 3011361496339065143296, 66249952919459433152512, 1457498964228107529355264, 32064977213018365645815808, 705429498686404044207947776

Offset

0,2

Comments

Same as Pisot sequences E(1, 22), L(1, 22), P(1, 22), T(1, 22). Essentially same as Pisot sequences E(22, 484), L(22, 484), P(22, 484), T(22, 484). 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 22-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 (22).

Formula

G.f.: 1/(1-22*x). - Philippe Deléham, Nov 23 2008

a(n) = 22^n; a(n) = 22*a(n-1) n>0 a(0)=1. [Vincenzo Librandi, Nov 21 2010]

Mathematica

NestList[22#&, 1, 20] (* Harvey P. Dale, Apr 22 2022 *)

Prog

(Sage) [lucas_number1(n, 22, 0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009
(Magma)[22^n: n in [0..100]] // Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=22^n \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Sequence in context: A223784 A223970 A171296 * A285876 A041221 A041926

Adjacent sequences: A009963 A009964 A009965 * A009967 A009968 A009969

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved