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%I #52 Jul 12 2023 12:39:39
%S 1,32,1024,32768,1048576,33554432,1073741824,34359738368,
%T 1099511627776,35184372088832,1125899906842624,36028797018963968,
%U 1152921504606846976,36893488147419103232,1180591620717411303424
%N Powers of 32.
%C Same as Pisot sequences E(1, 32), L(1, 32), P(1, 32), T(1, 32). Essentially same as Pisot sequences E(32, 1024), L(32, 1024), P(32, 1024), T(32, 1024). See A008776 for definitions of Pisot sequences.
%C 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 32-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011
%H T. D. Noe, <a href="/A009976/b009976.txt">Table of n, a(n) for n = 0..100</a>
%H Philip DeOrsey, Stephen G. Hartke, and Jason Williford, <a href="https://arxiv.org/abs/2105.08300">A Classification of Hyperfocused 12-Arcs</a>, arXiv:2105.08300 [math.CO], 2021.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (32).
%F G.f.: 1/(1-32*x). - _Philippe Deléham_, Nov 24 2008
%F a(n) = 32^n; a(n) = 32*a(n-1) for n > 0, a(0)=1. - _Vincenzo Librandi_, Nov 21 2010
%e a(6) = 32^6 = 1073741824.
%p A009976:=n->32^n; seq(A009976(k), k=0..50); # _Wesley Ivan Hurt_, Nov 04 2013
%t Table[32^n, {n,0,50}] (* _Wesley Ivan Hurt_, Nov 04 2013 *)
%o (Sage) [lucas_number1(n,32,0) for n in range(1, 17)]# - _Zerinvary Lajos_, Nov 07 2009
%o (Magma)[32^n: n in [0..100]] - _Vincenzo Librandi_, Nov 21 2010
%o (Maxima) A009976(n):=32^n$
%o makelist(A009976(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%o (PARI) a(n)=32^n \\ _Charles R Greathouse IV_, Sep 24 2015
%o (Python)
%o def A009976(n): return 1<<5*n # _Chai Wah Wu_, Nov 10 2022
%Y Subsequence of A000079.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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