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 A194431 #30 Jun 06 2025 14:46:06
%S A194431 1,19,53,103,169,251,349,463,593,739,901,1079,1273,1483,1709,1951,
%T A194431 2209,2483,2773,3079,3401,3739,4093,4463,4849,5251,5669,6103,6553,
%U A194431 7019,7501,7999,8513,9043,9589,10151,10729,11323,11933,12559,13201,13859,14533,15223,15929
%N A194431 a(n) = 8*n^2 - 6*n - 1.
%C A194431 Sequence found by reading the line from 1, in the direction 1, 19, ..., in the square spiral whose vertices are the triangular numbers A000217.
%H A194431 Vincenzo Librandi, <a href="/A194431/b194431.txt">Table of n, a(n) for n = 1..10000</a>
%H A194431 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A194431 G.f.: x*(-1 - 16*x + x^2)/(x-1)^3. - _R. J. Mathar_, Sep 06 2011
%F A194431 From _Elmo R. Oliveira_, Jun 04 2025: (Start)
%F A194431 E.g.f.: 1 + (-1 + 2*x + 8*x^2)*exp(x).
%F A194431 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%t A194431 Table[8n^2-6n-1,{n,50}] (* or *) LinearRecurrence[{3,-3,1},{1,19,53},50] (* _Harvey P. Dale_, May 29 2021 *)
%o A194431 (Magma) [8*n^2 - 6*n - 1: n in [1..50]]; // _Vincenzo Librandi_, Sep 07 2011
%o A194431 (PARI) a(n)=8*n^2-6*n-1 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A194431 Cf. A000217, A014634, A051870, A069129, A139098, A194268.
%K A194431 nonn,easy
%O A194431 1,2
%A A194431 _Omar E. Pol_, Sep 05 2011