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 A195025 #44 Dec 30 2024 12:03:30
%S A195025 0,17,62,135,236,365,522,707,920,1161,1430,1727,2052,2405,2786,3195,
%T A195025 3632,4097,4590,5111,5660,6237,6842,7475,8136,8825,9542,10287,11060,
%U A195025 11861,12690,13547,14432,15345,16286,17255,18252,19277,20330,21411,22520,23657,24822,26015
%N A195025 a(n) = n*(14*n + 3).
%C A195025 Sequence found by reading the line from 0, in the direction 0, 17, ..., 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].
%C A195025 a(k) is a square for k = (3/56)*((449 + 120*sqrt(14))^n + (449 - 120*sqrt(14))^n - 2). - _Bruno Berselli_, Oct 18 2011
%H A195025 Vincenzo Librandi, <a href="/A195025/b195025.txt">Table of n, a(n) for n = 0..10000</a>
%H A195025 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A195025 a(n) = 14*n^2 + 3*n.
%F A195025 G.f.: x*(17+11*x)/(1-x)^3. - _Bruno Berselli_, Oct 18 2011
%F A195025 From _Elmo R. Oliveira_, Dec 30 2024: (Start)
%F A195025 E.g.f.: exp(x)*x*(17 + 14*x).
%F A195025 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3. (End)
%t A195025 Table[n(14n+3),{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{0,17,62},50] (* _Harvey P. Dale_, Jul 17 2023 *)
%o A195025 (Magma) [14*n^2 +3*n: n in [0..50]]; // _Vincenzo Librandi_, Oct 14 2011
%o A195025 (PARI) a(n)=n*(14*n+3) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A195025 Cf. A144555, A152760, A185019, A193053, A195019, A195020, A195023, A195024, A195320.
%K A195025 nonn,easy
%O A195025 0,2
%A A195025 _Omar E. Pol_, Oct 13 2011
%E A195025 Name suggested by _Bruno Berselli_, Oct 13 2011