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%I A153875 #24 Sep 01 2016 02:28:06
%S A153875 0,3,39,108,210,345,513,714,948,1215,1515,1848,2214,2613,3045,3510,
%T A153875 4008,4539,5103,5700,6330,6993,7689,8418,9180,9975,10803,11664,12558,
%U A153875 13485,14445,15438,16464,17523,18615,19740,20898,22089
%N A153875 3 times 13-gonal (or tridecagonal) numbers: 3*n*(11*n - 9)/2.
%H A153875 G. C. Greubel, <a href="/A153875/b153875.txt">Table of n, a(n) for n = 0..1000</a>
%H A153875 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A153875 a(n) = (33*n^2 - 27*n)/2 = A051865(n)*3.
%F A153875 a(n) = a(n-1) + 33*n - 30, with n>0, a(0)=0. - _Vincenzo Librandi_, Dec 14 2010
%F A153875 G.f.: 3*x*(1 + 10*x)/(1-x)^3. - _Bruno Berselli_, Jan 21 2011
%F A153875 From _G. C. Greubel_, Aug 31 2016: (Start)
%F A153875 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A153875 E.g.f.: (3/2)*x*(2 + 11*x)*exp(x). (End)
%t A153875 s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,3,7!,33}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 02 2009 *)
%t A153875 LinearRecurrence[{3, -3, 1}, {0, 3, 39}, 25] (* or *) Table[33*n^2 - 27*n)/2, {n,0,25}] (* _G. C. Greubel_, Aug 31 2016 *)
%o A153875 (PARI) a(n)=3*n*(11*n-9)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A153875 Cf. A051865, A152997.
%Y A153875 3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152773, A152751, A152759, A152767, A153783, A153448.
%Y A153875 Cf. numbers of the form n*(n*k-k+6))/2, this sequence is the case k=33: see Comments lines of A226492.
%K A153875 nonn,easy
%O A153875 0,2
%A A153875 _Omar E. Pol_, Jan 03 2009

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