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 A152759 #42 Dec 15 2024 11:02:07
%S A152759 0,3,27,72,138,225,333,462,612,783,975,1188,1422,1677,1953,2250,2568,
%T A152759 2907,3267,3648,4050,4473,4917,5382,5868,6375,6903,7452,8022,8613,
%U A152759 9225,9858,10512,11187,11883,12600,13338,14097,14877,15678,16500,17343,18207,19092,19998
%N A152759 3 times 9-gonal (or nonagonal) numbers: a(n) = 3*n*(7*n-5)/2.
%H A152759 Vincenzo Librandi, <a href="/A152759/b152759.txt">Table of n, a(n) for n = 0..1000</a>
%H A152759 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A152759 a(n) = (21*n^2 - 15*n)/2 = 3*A001106(n).
%F A152759 a(n) = a(n-1) + 21*n - 18 with n > 0, a(0)=0. - _Vincenzo Librandi_, Nov 26 2010
%F A152759 G.f.: 3*x*(1+6*x)/(1-x)^3. - _Bruno Berselli_, Jan 21 2011
%F A152759 a(n) = n + A226491(n). - _Bruno Berselli_, Jun 11 2013
%F A152759 From _Elmo R. Oliveira_, Dec 15 2024: (Start)
%F A152759 E.g.f.: 3*exp(x)*x*(2 + 7*x)/2.
%F A152759 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A152759 s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,3,6!,21}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 02 2009 *)
%t A152759 CoefficientList[Series[3 x (1 + 6 x) / (1 - x)^3, {x, 0, 60}], x] (* _Vincenzo Librandi_, Jun 05 2013 *)
%t A152759 LinearRecurrence[{3,-3,1},{0,3,27},40] (* _Harvey P. Dale_, May 26 2015 *)
%o A152759 (PARI) a(n)=3*n*(7*n-5)/2 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A152759 Cf. A001106, A139268, A226491.
%Y A152759 3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152773, A152751, A152767, A153783, A153448, A153875.
%Y A152759 Cf. numbers of the form n*(n*k-k+6)/2, this sequence is the case k=21: see Comments lines of A226492.
%K A152759 nonn,easy
%O A152759 0,2
%A A152759 _Omar E. Pol_, Dec 14 2008