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 A202804 #54 Dec 12 2024 14:41:06
%S A202804 0,10,32,66,112,170,240,322,416,522,640,770,912,1066,1232,1410,1600,
%T A202804 1802,2016,2242,2480,2730,2992,3266,3552,3850,4160,4482,4816,5162,
%U A202804 5520,5890,6272,6666,7072,7490,7920,8362,8816,9282,9760,10250,10752,11266,11792,12330
%N A202804 a(n) = n*(6*n+4).
%C A202804 Sequence found by reading the line from 0, in the direction 0, 10, ..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. Opposite numbers to the members of A033579 in the same spiral. - _Omar E. Pol_, Jul 17 2012
%C A202804 Partial sums give A163815. - _Leo Tavares_, Feb 25 2022
%H A202804 Jeremy Gardiner, <a href="/A202804/b202804.txt">Table of n, a(n) for n = 0..3000</a>
%H A202804 Milan Janjic and Boris Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv 1301.4550 [math.CO], 2013.
%H A202804 Leo Tavares, <a href="/A202804/a202804.jpg">Illustration: Star Halves</a>.
%H A202804 Pavlos Vavolas, <a href="http://www.dcs.shef.ac.uk/intranet/teaching/projects/archive/msc2005/pdf/m4pv.pdf">Cellular automaton model of cardiac arrhythmias</a>, University of Sheffield Department of Computer Science (2005), (see page 43). [broken link, <a href="http://www.dcs.shef.ac.uk/intranet/archive/public/2004_2005/projects/msc/m4pv.html">abstract</a>]
%H A202804 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A202804 a(n) = 2*n(3*n+2) = 6*n^2 + 4*n = 2*A045944(n).
%F A202804 a(n) = A080859(n) - 1. - _Omar E. Pol_, Jul 18 2012
%F A202804 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Dec 28 2015
%F A202804 G.f.: 2*x*(5 + x)/(1 - x)^3. - _Indranil Ghosh_, Apr 10 2017
%F A202804 a(n) = A003154(n+1) - A005408(n). - _Leo Tavares_, Feb 25 2022
%F A202804 From _Amiram Eldar_, Mar 01 2022: (Start)
%F A202804 Sum_{n>=1} 1/a(n) = (Pi/sqrt(3) - 3*log(3) + 3)/8.
%F A202804 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(4*sqrt(3)) - 3/8. (End)
%F A202804 E.g.f.: 2*exp(x)*x*(5 + 3*x). - _Elmo R. Oliveira_, Dec 12 2024
%p A202804 A202804:=n->n*(6*n+4): seq(A202804(n), n=0..100); # _Wesley Ivan Hurt_, Apr 09 2017
%t A202804 Table[n(6n+4),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,10,32},50] (* _Harvey P. Dale_, Dec 28 2015 *)
%o A202804 (PARI) x='x + O('x^50); concat([0], Vec(-2*x*(5 + x)/(x - 1)^3)) \\ _Indranil Ghosh_, Apr 10 2017
%Y A202804 Cf. A003154, A005408, A033580, A033581, A049453, A163815, A195319.
%Y A202804 Cf. A001318, A033579, A045944, A080859.
%K A202804 nonn,easy
%O A202804 0,2
%A A202804 _Jeremy Gardiner_, Dec 24 2011