This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A009976 #62 Jul 08 2025 22:24:21
%S A009976 1,32,1024,32768,1048576,33554432,1073741824,34359738368,
%T A009976 1099511627776,35184372088832,1125899906842624,36028797018963968,
%U A009976 1152921504606846976,36893488147419103232,1180591620717411303424,37778931862957161709568,1208925819614629174706176,38685626227668133590597632
%N A009976 Powers of 32.
%C A009976 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 A009976 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 A009976 T. D. Noe, <a href="/A009976/b009976.txt">Table of n, a(n) for n = 0..100</a>
%H A009976 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 A009976 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A009976 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (32).
%F A009976 G.f.: 1/(1-32*x). - _Philippe Deléham_, Nov 24 2008
%F A009976 a(n) = 32^n; a(n) = 32*a(n-1) for n > 0, a(0)=1. - _Vincenzo Librandi_, Nov 21 2010
%F A009976 From _Elmo R. Oliveira_, Jul 08 2025: (Start)
%F A009976 E.g.f.: exp(32*x).
%F A009976 a(n) = 2^A008587(n) = A000079(n)*A001025(n) = A089357(n)/A000079(n). (End)
%e A009976 a(6) = 32^6 = 1073741824.
%p A009976 A009976:=n->32^n; seq(A009976(k), k=0..50); # _Wesley Ivan Hurt_, Nov 04 2013
%t A009976 Table[32^n, {n,0,50}] (* _Wesley Ivan Hurt_, Nov 04 2013 *)
%o A009976 (SageMath) [lucas_number1(n,32,0) for n in range(1, 17)] # _Zerinvary Lajos_, Nov 07 2009
%o A009976 (Magma) [32^n: n in [0..100]]; // _Vincenzo Librandi_, Nov 21 2010
%o A009976 (Maxima) A009976(n):=32^n$
%o A009976 makelist(A009976(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%o A009976 (PARI) a(n)=32^n \\ _Charles R Greathouse IV_, Sep 24 2015
%o A009976 (Python)
%o A009976 def A009976(n): return 1<<5*n # _Chai Wah Wu_, Nov 10 2022
%Y A009976 Subsequence of A000079.
%Y A009976 Cf. A001025, A008587, A008776, A089357.
%K A009976 nonn,easy
%O A009976 0,2
%A A009976 _N. J. A. Sloane_