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 A195021 #62 Jan 15 2025 10:23:32
%S A195021 0,3,34,93,180,295,438,609,808,1035,1290,1573,1884,2223,2590,2985,
%T A195021 3408,3859,4338,4845,5380,5943,6534,7153,7800,8475,9178,9909,10668,
%U A195021 11455,12270,13113,13984,14883,15810,16765,17748,18759,19798,20865,21960,23083,24234,25413
%N A195021 a(n) = n*(14*n - 11).
%C A195021 Sequence found by reading the first two vertices [0, 3] together with the line from 34, in the direction 34, 93, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020, which is related to the primitive Pythagorean triple [3, 4, 5]. For another version see A195030.
%H A195021 Vincenzo Librandi, <a href="/A195021/b195021.txt">Table of n, a(n) for n = 0..10000</a>
%H A195021 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A195021 a(n) = 14*n^2 - 11*n.
%F A195021 From _Colin Barker_, Apr 09 2012: (Start)
%F A195021 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A195021 G.f.: x*(3+25*x)/(1-x)^3. (End)
%F A195021 E.g.f.: exp(x)*x*(3 + 14*x). - _Elmo R. Oliveira_, Dec 30 2024
%t A195021 Table[n*(14*n - 11), {n, 0, 50}] (* _Paolo Xausa_, Jan 15 2025 *)
%o A195021 (Magma) [14*n^2 - 11*n: n in [0..50]]; // _Vincenzo Librandi_, Oct 14 2011
%o A195021 (PARI) a(n)=n*(14*n-11) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A195021 Cf. A144555, A185019, A193053, A195019, A195020, A195023, A195024, A195025, A195030, A195320, A198017.
%Y A195021 Cf. numbers of the form n*(n*k - k + 6)/2, this sequence is the case k=28: see Comments lines of A226492.
%K A195021 nonn,easy
%O A195021 0,2
%A A195021 _Omar E. Pol_, Sep 07 2011
%E A195021 Edited by _Bruno Berselli_, Oct 18 2011