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 A153783 #28 Oct 05 2024 09:40:02
%S A153783 0,3,33,90,174,285,423,588,780,999,1245,1518,1818,2145,2499,2880,3288,
%T A153783 3723,4185,4674,5190,5733,6303,6900,7524,8175,8853,9558,10290,11049,
%U A153783 11835,12648,13488,14355,15249,16170,17118,18093,19095
%N A153783 3 times 11-gonal (or hendecagonal) numbers: a(n) = 3*n*(9*n-7)/2.
%H A153783 G. C. Greubel, <a href="/A153783/b153783.txt">Table of n, a(n) for n = 0..1000</a>
%H A153783 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A153783 a(n) = (27*n^2 - 21*n)/2 = A051682(n)*3.
%F A153783 a(n) = 27*n + a(n-1) - 24, with n>0, a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F A153783 G.f.: 3*x*(1 + 8*x)/(1-x)^3. - _Bruno Berselli_, Jan 21 2011
%F A153783 From _G. C. Greubel_, Aug 28 2016: (Start)
%F A153783 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A153783 E.g.f.: (3/2)*x*(2 + 9*x)*exp(x). (End)
%t A153783 s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,3,6!,27}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 02 2009 *)
%t A153783 Table[3*n*(9*n-7)/2, {n,0,25}] (* or *) LinearRecurrence[{3,-3,1},{0,3,33},25] (* _G. C. Greubel_, Aug 28 2016 *)
%o A153783 (PARI) a(n)=3*n*(9*n-7)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A153783 Cf. A051682, A152995.
%Y A153783 3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152773, A152751, A152759, A152767, A153448, A153875.
%Y A153783 Cf. numbers of the form n*(n*k-k+6)/2, this sequence is the case k=27: see Comments lines of A226492.
%K A153783 easy,nonn
%O A153783 0,2
%A A153783 _Omar E. Pol_, Jan 02 2009