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 A194268 #28 Oct 22 2024 16:26:58
%S A194268 1,16,47,94,157,236,331,442,569,712,871,1046,1237,1444,1667,1906,2161,
%T A194268 2432,2719,3022,3341,3676,4027,4394,4777,5176,5591,6022,6469,6932,
%U A194268 7411,7906,8417,8944,9487,10046,10621,11212,11819,12442,13081,13736,14407,15094,15797
%N A194268 a(n) = 8*n^2 + 7*n + 1.
%C A194268 Sequence found by reading the line from 1, in the direction 1, 16,..., in the square spiral whose vertices are the triangular numbers A000217.
%H A194268 Vincenzo Librandi, <a href="/A194268/b194268.txt">Table of n, a(n) for n = 0..10000</a>
%H A194268 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A194268 a(0)=1, a(1)=16, a(2)=47, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Apr 06 2014
%F A194268 From _Elmo R. Oliveira_, Oct 22 2024: (Start)
%F A194268 G.f.: (1 + 13*x + 2*x^2)/(1 - x)^3.
%F A194268 E.g.f.: (1 + 15*x + 8*x^2)*exp(x). (End)
%p A194268 A194268:=n->8*n^2+7*n+1: seq(A194268(n), n=0..50); # _Wesley Ivan Hurt_, Jul 15 2014
%t A194268 Table[8n^2+7n+1,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{1,16,47},50] (* _Harvey P. Dale_, Apr 06 2014 *)
%o A194268 (Magma) [8*n^2 +7*n + 1: n in [0..50]]; // _Vincenzo Librandi_, Sep 07 2011
%o A194268 (PARI) a(n)=8*n^2+7*n+1 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A194268 Cf. A000217, A014634, A051870, A069129, A139098, A194431.
%K A194268 nonn,easy
%O A194268 0,2
%A A194268 _Omar E. Pol_, Sep 05 2011