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%I #86 Mar 11 2024 13:04:55
%S 0,12,24,36,48,60,72,84,96,108,120,132,144,156,168,180,192,204,216,
%T 228,240,252,264,276,288,300,312,324,336,348,360,372,384,396,408,420,
%U 432,444,456,468,480,492,504,516,528,540,552,564,576,588,600,612,624,636
%N Multiples of 12: a(n) = 12*n.
%C Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 36 ).
%C The positive terms are the differences of consecutive star numbers (A003154). - _Mihir Mathur_, Jun 07 2013
%C A089911(a(n)) = 0. - _Reinhard Zumkeller_, Jul 05 2013
%C a(1) = 12 is a primitive abundant number, thus all a(n), n >= 2, are nonprimitive abundant numbers. - _Daniel Forgues_, Sep 24 2016
%H Vincenzo Librandi, <a href="/A008594/b008594.txt">Table of n, a(n) for n = 0..2000</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=324">Encyclopedia of Combinatorial Structures 324</a>
%H 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 William A. Stein, <a href="http://wstein.org/Tables/dimskg0n.gp">Dimensions of the spaces S_k(Gamma_0(N))</a>
%H William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Star_number">Star Number</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 12*n. a(n) = 2*a(n-1)-a(n-2) for n>1. G.f.: 12*x/(1-x)^2. - _Vincenzo Librandi_, Jun 11 2011
%F a(n) = A003154(n)- A003154(n-1). - _Mihir Mathur_, Jun 07 2013
%p A008594:=n->12*n: seq(A008594(n), n=0..100); # _Wesley Ivan Hurt_, Sep 24 2016
%t 12*Range[0,200] (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2011 *)
%t NestList[12+#&,0,60] (* _Harvey P. Dale_, Feb 02 2022 *)
%o (Magma) [12*n: n in [0..50]]; // _Vincenzo Librandi_, Jun 11 2011
%o (Haskell)
%o a008594 = (* 12)
%o a008594_list = [0, 12 ..] -- _Reinhard Zumkeller_, Dec 12 2012
%o (PARI) a(n)=12*n \\ _Charles R Greathouse IV_, Apr 21 2015
%Y Subsequence of A072065 and A121032.
%Y Cf. A008592, A008593, A003154.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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