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%I #36 Sep 08 2022 08:45:39
%S 0,2,24,66,128,210,312,434,576,738,920,1122,1344,1586,1848,2130,2432,
%T 2754,3096,3458,3840,4242,4664,5106,5568,6050,6552,7074,7616,8178,
%U 8760,9362,9984,10626,11288,11970,12672,13394,14136,14898,15680
%N Twice 12-gonal numbers: a(n) = 2*n*(5*n-4).
%H Vincenzo Librandi, <a href="/A152965/b152965.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 2 * A051624(n).
%F G.f.: 2*x*(1+9*x)/(1-x)^3. - _Vincenzo Librandi_, Jul 10 2012
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Jul 10 2012
%t s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,2,6!,20}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 02 2009 *)
%t Table[10*n^2-8*n,{n,0,50}] (* _Vincenzo Librandi_, Jul 10 2012 *)
%t LinearRecurrence[{3,-3,1},{0,2,24},60] (* _Harvey P. Dale_, Apr 18 2016 *)
%o (Magma) [10*n^2-8*n: n in [0..50]]; // _Klaus Brockhaus_, Nov 27 2010
%o (PARI) a(n)=2*n*(5*n-4) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A051624 (12-gonal numbers).
%Y Cf. numbers of the form n*(n*k - k + 4))/2 listed in A226488 (this sequence is the case k=20). - _Bruno Berselli_, Jun 10 2013
%K easy,nonn
%O 0,2
%A _Omar E. Pol_, Dec 21 2008
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