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A009966 Powers of 22.

%I A009966 #50 Jul 09 2025 09:53:28
%S A009966 1,22,484,10648,234256,5153632,113379904,2494357888,54875873536,
%T A009966 1207269217792,26559922791424,584318301411328,12855002631049216,
%U A009966 282810057883082752,6221821273427820544,136880068015412051968,3011361496339065143296,66249952919459433152512,1457498964228107529355264,32064977213018365645815808,705429498686404044207947776
%N A009966 Powers of 22.
%C A009966 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.
%C A009966 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
%H A009966 T. D. Noe, <a href="/A009966/b009966.txt">Table of n, a(n) for n = 0..100</a>
%H A009966 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A009966 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (22).
%F A009966 G.f.: 1/(1-22*x). - _Philippe Deléham_, Nov 23 2008
%F A009966 a(n) = 22^n; a(n) = 22*a(n-1) n>0 a(0)=1. - _Vincenzo Librandi_, Nov 21 2010
%F A009966 From _Elmo R. Oliveira_, Jul 08 2025: (Start)
%F A009966 E.g.f.: exp(22*x).
%F A009966 a(n) = A000079(n)*A001020(n) = A009988(n)/A000079(n). (End)
%t A009966 NestList[22#&,1,20] (* _Harvey P. Dale_, Apr 22 2022 *)
%o A009966 (Sage) [lucas_number1(n,22,0) for n in range(1, 17)] # _Zerinvary Lajos_, Apr 29 2009
%o A009966 (Magma)[22^n: n in [0..100]]; // _Vincenzo Librandi_, Nov 21 2010
%o A009966 (PARI) a(n)=22^n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A009966 Cf. A000079, A001020, A008776, A009988.
%K A009966 nonn,easy
%O A009966 0,2
%A A009966 _N. J. A. Sloane_