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 A153786 #22 Oct 05 2024 14:38:49
%S A153786 0,6,42,108,204,330,486,672,888,1134,1410,1716,2052,2418,2814,3240,
%T A153786 3696,4182,4698,5244,5820,6426,7062,7728,8424,9150,9906,10692,11508,
%U A153786 12354,13230,14136,15072,16038,17034,18060,19116,20202,21318
%N A153786 6 times heptagonal numbers: a(n) = 3*n*(5*n-3).
%H A153786 G. C. Greubel, <a href="/A153786/b153786.txt">Table of n, a(n) for n = 0..1000</a>
%H A153786 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A153786 a(n) = 15*n^2 - 9*n = A000566(n)*6 = A135706(n)*3 = A152773(n)*2.
%F A153786 a(n) = 30*n + a(n-1) - 24 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F A153786 From _G. C. Greubel_, Aug 28 2016: (Start)
%F A153786 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A153786 G.f.: 6*x*(1 + 4*x)/(1 - x)^3.
%F A153786 E.g.f.: 3*x*(2 + 5*x)*exp(x). (End)
%t A153786 s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,6,8!,30}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 03 2009 *)
%t A153786 Table[ 3*n*(5*n-3), {n,0,25}] (* or *) LinearRecurrence[{3,-3,1},{0,6,42}, 25] (* _G. C. Greubel_, Aug 28 2016 *)
%o A153786 (PARI) a(n) = 3*n*(5*n-3); \\ _Michel Marcus_, Aug 28 2016
%Y A153786 Cf. A000566, A135706, A152773, A152777, A153785.
%K A153786 nonn,easy
%O A153786 0,2
%A A153786 _Omar E. Pol_, Jan 02 2009