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 A195023 #49 Jan 12 2025 16:37:54
%S A195023 0,10,48,114,208,330,480,658,864,1098,1360,1650,1968,2314,2688,3090,
%T A195023 3520,3978,4464,4978,5520,6090,6688,7314,7968,8650,9360,10098,10864,
%U A195023 11658,12480,13330,14208,15114,16048,17010,18000,19018,20064,21138,22240,23370,24528,25714
%N A195023 a(n) = 14*n^2 - 4*n.
%C A195023 Sequence found by reading the line from 0, in the direction 0, 10, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. This is the one of the semi-axis of the square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].
%H A195023 Vincenzo Librandi, <a href="/A195023/b195023.txt">Table of n, a(n) for n = 0..10000</a>
%H A195023 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A195023 a(n) = 2*A135703(n). - _Bruno Berselli_, Oct 13 2011
%F A195023 From _Colin Barker_, Apr 09 2012: (Start)
%F A195023 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A195023 G.f.: 2*x*(5+9*x)/(1-x)^3. (End)
%F A195023 E.g.f.: 2*exp(x)*x*(5 + 7*x). - _Elmo R. Oliveira_, Dec 30 2024
%t A195023 Table[14n^2-4n,{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{0,10,48},50] (* _Harvey P. Dale_, Sep 05 2012 *)
%o A195023 (Magma) [14*n^2 - 4*n: n in [0..50]]; // _Vincenzo Librandi_, Oct 14 2011
%o A195023 (PARI) a(n)=14*n^2-4*n \\ _Charles R Greathouse IV_, Apr 10 2012
%Y A195023 Cf. A135703, A144555, A152760, A193053, A195019, A195020, A195024, A195320, A198017.
%K A195023 nonn,easy
%O A195023 0,2
%A A195023 _Omar E. Pol_, Oct 13 2011
%E A195023 Corrected by _Vincenzo Librandi_, Oct 14 2011