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 A139268 #40 Dec 27 2024 21:03:37
%S A139268 0,2,18,48,92,150,222,308,408,522,650,792,948,1118,1302,1500,1712,
%T A139268 1938,2178,2432,2700,2982,3278,3588,3912,4250,4602,4968,5348,5742,
%U A139268 6150,6572,7008,7458,7922,8400,8892,9398,9918,10452,11000
%N A139268 Twice nonagonal numbers (or twice 9-gonal numbers): a(n) = n*(7*n-5).
%H A139268 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A139268 a(n) = 2*A001106(n) = 7*n^2 - 5*n = n*(7*n-5).
%F A139268 a(n) = 14*n + a(n-1) - 12, with a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F A139268 G.f.: 2*x*(1 + 6*x)/(1 - x)^3. - _Philippe Deléham_, Apr 03 2013
%F A139268 From _Elmo R. Oliveira_, Dec 27 2024: (Start)
%F A139268 E.g.f.: exp(x)*x*(2 + 7*x).
%F A139268 a(n) = n + A051868(n).
%F A139268 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A139268 s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,2,6!,14}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 02 2009 *)
%t A139268 2*PolygonalNumber[9,Range[0,40]] (* or *) LinearRecurrence[{3,-3,1},{0,2,18},50] (* _Harvey P. Dale_, Feb 08 2024 *)
%o A139268 (PARI) a(n)=n*(7*n-5) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A139268 Cf. A001106, A051868.
%Y A139268 Cf. numbers of the form n*(n*k - k + 4)/2 listed in A226488 (this sequence is the case k=14). - _Bruno Berselli_, Jun 10 2013
%K A139268 nonn,easy
%O A139268 0,2
%A A139268 _Omar E. Pol_, May 15 2008