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 A001021 M4869 N2084 #90 Apr 28 2024 11:32:16
%S A001021 1,12,144,1728,20736,248832,2985984,35831808,429981696,5159780352,
%T A001021 61917364224,743008370688,8916100448256,106993205379072,
%U A001021 1283918464548864,15407021574586368,184884258895036416,2218611106740436992
%N A001021 Powers of 12.
%C A001021 Same as Pisot sequences E(1, 12), L(1, 12), P(1, 12), T(1, 12). Essentially same as Pisot sequences E(12, 144), L(12, 144), P(12, 144), T(12, 144). See A008776 for definitions of Pisot sequences.
%C A001021 Central terms of the triangle in A100851. - _Reinhard Zumkeller_, Mar 04 2006
%C A001021 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 12-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011
%C A001021 Starting with 12, this sequence appears in the film "Vollmond" (1998, dir. Fredi Murer), when the children write it on the sidewalk at night. - _Alonso del Arte_, Dec 21 2011
%D A001021 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001021 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001021 T. D. Noe, <a href="/A001021/b001021.txt">Table of n, a(n) for n = 0..100</a>
%H A001021 P. J. Cameron, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/groups.html">Sequences realized by oligomorphic permutation groups</a>, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
%H A001021 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=276">Encyclopedia of Combinatorial Structures 276</a>.
%H A001021 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A001021 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A001021 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992.
%H A001021 Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">Arithmetic and growth of periodic orbits</a>, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
%H A001021 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (12).
%F A001021 G.f.: 1/(1-12*x).
%F A001021 E.g.f.: exp(12x).
%F A001021 a(n) = 12*a(n-1). - _Zerinvary Lajos_, Apr 27 2009
%F A001021 a(n) = A159991(n)/A000351(n). - _Reinhard Zumkeller_, May 02 2009
%F A001021 From _Reinhard Zumkeller_, Mar 31 2012: (Start)
%F A001021 a(n) = A000302(n) * A000244(n). - _Reinhard Zumkeller_, Mar 31 2012
%F A001021 A001222(a(n)) = A008585(n); A000005(a(n)) = A000384(a(n)). (End)
%F A001021 a(n) = det(|ps(i+2, j)|, 1 <= i, j <= n), where ps(n, k) are Legendre-Stirling numbers of the first kind. - _Mircea Merca_, Apr 04 2013
%p A001021 A001021:=-1/(-1+12*z); # _Simon Plouffe_ in his 1992 dissertation
%t A001021 Table[12^n, {n, 0, 40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 15 2011 *)
%o A001021 (PARI) a(n)=12^n \\ _Charles R Greathouse IV_, Dec 21 2011
%o A001021 (Haskell)
%o A001021 a001021 = (12 ^)
%o A001021 a001021_list = iterate (* 12) 1 -- _Reinhard Zumkeller_, Mar 31 2012
%Y A001021 Cf. A024140 and A178248, 12^n +/- 1; A016125.
%Y A001021 Cf. A000005, A000244, A000302, A000351, A000384, A001222, A008585, A008776, A100851, A159991.
%K A001021 nonn,easy
%O A001021 0,2
%A A001021 _N. J. A. Sloane_