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 A153784 #35 Dec 15 2024 15:46:59
%S A153784 0,4,28,72,136,220,324,448,592,756,940,1144,1368,1612,1876,2160,2464,
%T A153784 2788,3132,3496,3880,4284,4708,5152,5616,6100,6604,7128,7672,8236,
%U A153784 8820,9424,10048,10692,11356,12040,12744,13468,14212,14976,15760,16564,17388,18232,19096
%N A153784 4 times heptagonal numbers: a(n) = 2*n*(5*n-3).
%C A153784 Sequence found by reading the line from 0, in the direction 0, 4, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - _Omar E. Pol_, Jul 18 2012
%H A153784 Ivan Panchenko, <a href="/A153784/b153784.txt">Table of n, a(n) for n = 0..1000</a>
%H A153784 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A153784 a(n) = 10*n^2 - 6*n = 4*A000566(n) = 2*A135706(n).
%F A153784 a(n) = 20*n + a(n-1) - 16 (with a(0)=0). - _Vincenzo Librandi_, Aug 03 2010
%F A153784 a(n) = A087348(n) - 1, n >= 1. - _Omar E. Pol_, Jul 18 2012
%F A153784 a(0)=0, a(1)=4, a(2)=28, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Mar 19 2015
%F A153784 From _Elmo R. Oliveira_, Dec 15 2024: (Start)
%F A153784 G.f.: 4*x*(1 + 4*x)/(1 - x)^3.
%F A153784 E.g.f.: 2*exp(x)*x*(2 + 5*x).
%F A153784 a(n) = A152745(n) - n. (End)
%t A153784 s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,4,6!,20}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 02 2009 *)
%t A153784 Table[2n(5n-3),{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{0,4,28},50] (* _Harvey P. Dale_, Mar 19 2015 *)
%o A153784 (PARI) a(n)=2*n*(5*n-3) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A153784 Cf. A000566, A085787, A087348, A135706, A152745, A152773.
%K A153784 easy,nonn
%O A153784 0,2
%A A153784 _Omar E. Pol_, Jan 02 2009