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A008594 Multiples of 12.

%I A008594 #90 Apr 10 2025 16:34:48
%S A008594 0,12,24,36,48,60,72,84,96,108,120,132,144,156,168,180,192,204,216,
%T A008594 228,240,252,264,276,288,300,312,324,336,348,360,372,384,396,408,420,
%U A008594 432,444,456,468,480,492,504,516,528,540,552,564,576,588,600,612,624,636
%N A008594 Multiples of 12.
%C A008594 Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 36 ).
%C A008594 The positive terms are the differences of consecutive star numbers (A003154). - _Mihir Mathur_, Jun 07 2013
%C A008594 A089911(a(n)) = 0. - _Reinhard Zumkeller_, Jul 05 2013
%C A008594 a(1) = 12 is a primitive abundant number, thus all a(n), n >= 2, are nonprimitive abundant numbers. - _Daniel Forgues_, Sep 24 2016
%H A008594 Vincenzo Librandi, <a href="/A008594/b008594.txt">Table of n, a(n) for n = 0..2000</a>
%H A008594 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A008594 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=324">Encyclopedia of Combinatorial Structures 324</a>.
%H A008594 Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014.
%H A008594 William A. Stein, <a href="http://wstein.org/Tables/dimskg0n.gp">Dimensions of the spaces S_k(Gamma_0(N))</a>.
%H A008594 William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>.
%H A008594 Wikipedia, <a href="http://en.wikipedia.org/wiki/Star_number">Star Number</a>.
%H A008594 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A008594 From _Vincenzo Librandi_, Jun 11 2011: (Start)
%F A008594 a(n) = 12*n.
%F A008594 a(n) = 2*a(n-1) - a(n-2) for n > 1.
%F A008594 G.f.: 12*x/(1-x)^2. (End)
%F A008594 a(n) = A003154(n) - A003154(n-1). - _Mihir Mathur_, Jun 07 2013
%F A008594 From _Elmo R. Oliveira_, Apr 10 2025: (Start)
%F A008594 E.g.f.: 12*x*exp(x).
%F A008594 a(n) = 2*A008588(n) = A008606(n)/2. (End)
%p A008594 A008594:=n->12*n: seq(A008594(n), n=0..100); # _Wesley Ivan Hurt_, Sep 24 2016
%t A008594 12*Range[0,200] (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2011 *)
%t A008594 NestList[12+#&,0,60] (* _Harvey P. Dale_, Feb 02 2022 *)
%o A008594 (Magma) [12*n: n in [0..50]]; // _Vincenzo Librandi_, Jun 11 2011
%o A008594 (Haskell)
%o A008594 a008594 = (* 12)
%o A008594 a008594_list = [0, 12 ..]  -- _Reinhard Zumkeller_, Dec 12 2012
%o A008594 (PARI) a(n)=12*n \\ _Charles R Greathouse IV_, Apr 21 2015
%Y A008594 Subsequence of A072065 and A121032.
%Y A008594 Cf. A003154, A008588, A008592, A008593, A008606, A089911.
%K A008594 nonn,easy
%O A008594 0,2
%A A008594 _N. J. A. Sloane_