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A009966
Powers of 22.
12
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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved