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 A195024 #44 Jan 12 2025 19:26:54
%S A195024 0,13,54,123,220,345,498,679,888,1125,1390,1683,2004,2353,2730,3135,
%T A195024 3568,4029,4518,5035,5580,6153,6754,7383,8040,8725,9438,10179,10948,
%U A195024 11745,12570,13423,14304,15213,16150,17115,18108,19129,20178,21255,22360,23493,24654,25843
%N A195024 a(n) = n*(14*n - 1).
%C A195024 Related to the primitive Pythagorean triple [3, 4, 5].
%C A195024 Sequence found by reading the line from 0, in the direction 0, 13, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. This is the one of the semi-diagonals of the square spiral.
%C A195024 Also sequence found by reading the line from 0, in the direction 0, 13, ..., in the square spiral whose vertices are the generalized 9-gonal numbers A118277. - _Omar E. Pol_, Jul 28 2012
%H A195024 Vincenzo Librandi, <a href="/A195024/b195024.txt">Table of n, a(n) for n = 0..10000</a>
%H A195024 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A195024 a(n) = 14*n^2 - n.
%F A195024 From _Colin Barker_, Apr 09 2012: (Start)
%F A195024 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A195024 G.f.: x*(13+15*x)/(1-x)^3. (End)
%F A195024 E.g.f.: exp(x)*x*(13 + 14*x). - _Elmo R. Oliveira_, Jan 12 2025
%t A195024 Table[n(14n-1),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,13,54},50] (* _Harvey P. Dale_, Jul 28 2012 *)
%o A195024 (Magma) [14*n^2 - n: n in [0..50]]; // _Vincenzo Librandi_, Oct 14 2011
%o A195024 (PARI) a(n)=n*(14*n-1) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A195024 Cf. A118277, A144555, A152760, A185019, A193053, A195019, A195020, A195320, A198017.
%K A195024 nonn,easy
%O A195024 0,2
%A A195024 _Omar E. Pol_, Oct 13 2011