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 A139278 #29 Mar 17 2022 07:03:56
%S A139278 0,15,46,93,156,235,330,441,568,711,870,1045,1236,1443,1666,1905,2160,
%T A139278 2431,2718,3021,3340,3675,4026,4393,4776,5175,5590,6021,6468,6931,
%U A139278 7410,7905,8416,8943,9486,10045,10620,11211,11818,12441,13080
%N A139278 a(n) = n*(8*n+7).
%C A139278 Sequence found by reading the segment (0, 15) together with the line from 15, in the direction 15, 46, ..., in the square spiral whose vertices are the triangular numbers A000217.
%H A139278 G. C. Greubel, <a href="/A139278/b139278.txt">Table of n, a(n) for n = 0..5000</a>
%H A139278 Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.
%H A139278 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A139278 a(n) = 8*n^2 + 7*n.
%F A139278 Sequences of the form a(n)=8*n^2+c*n have generating functions x{c+8+(8-c)x} / (1-x)^3 and recurrence a(n)= 3a(n-1)-3a(n-2)+a(n-3). The inverse binomial transform is 0, c+8, 16, 0, 0, ... (0 continued). This applies to A139271-A139278, positive or negative c. - _R. J. Mathar_, May 12 2008
%F A139278 a(n) = 16*n+a(n-1)-1 (with a(0)=0). - _Vincenzo Librandi_, Aug 03 2010
%F A139278 From _G. C. Greubel_, Jul 18 2017: (Start)
%F A139278 G.f.: x*(x+15)/(1-x)^3.
%F A139278 E.g.f.: (8*x^2 + 15*x)*exp(x). (End)
%F A139278 Sum_{n>=1} 1/a(n) = 8/49 + (sqrt(2)+1)*Pi/14 - 4*log(2)/7 - sqrt(2)*log(sqrt(2)+1)/7. - _Amiram Eldar_, Mar 17 2022
%t A139278 Table[n (8 n + 7), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 15, 46}, 50] (* _Harvey P. Dale_, Oct 07 2015 *)
%o A139278 (PARI) a(n)=n*(8*n+7) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A139278 Cf. A000217, A014634, A014635, A033585, A033586, A033587, A035008, A051870, A069129, A085250, A072279, A139272, A139273, A139274, A139275, A139276, A139277, A139279, A139280, A139281, A139282.
%K A139278 nonn,easy
%O A139278 0,2
%A A139278 _Omar E. Pol_, Apr 26 2008