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 A271913 #32 Mar 03 2024 22:21:07
%S A271913 0,16,68,148,248,360,488,620,768,924,1096,1272,1464,1660,1872,2088,
%T A271913 2320,2556,2808,3064,3336,3612,3904,4200,4512,4828,5160,5496,5848,
%U A271913 6204,6576,6952,7344,7740,8152,8568,9000,9436,9888,10344,10816,11292,11784,12280,12792,13308,13840,14376,14928,15484
%N A271913 Number of ways to choose three distinct points from a 4 X n grid so that they form an isosceles triangle.
%H A271913 Chai Wah Wu, <a href="http://arxiv.org/abs/1605.00180">Counting the number of isosceles triangles in rectangular regular grids</a>, arXiv:1605.00180 [math.CO], 2016.
%H A271913 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, -2, 1).
%F A271913 Conjectured g.f.: 4*x*(x^10-x^8+2*x^6+x^5+4*x^4+4*x^3-3*x^2-9*x-4)/((x+1)*(x-1)^3).
%F A271913 Conjectured recurrence: a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n > 12.
%F A271913 Conjectures from _Colin Barker_, Apr 25 2016: (Start)
%F A271913 a(n) = -3/2*(143+(-1)^n)+64*n+5*n^2 for n>8.
%F A271913 a(n) = 5*n^2+64*n-216 for n>8 and even.
%F A271913 a(n) = 5*n^2+64*n-213 for n>8 and odd.
%F A271913 (End)
%F A271913 The conjectured g.f. and recurrence are true. See paper in links. - _Chai Wah Wu_, May 07 2016
%t A271913 Join[{0, 16, 68, 148, 248, 360, 488, 620}, LinearRecurrence[{2, 0, -2, 1}, {768, 924, 1096, 1272}, 42]] (* _Jean-François Alcover_, Sep 03 2018 *)
%Y A271913 Row 4 of A271910.
%Y A271913 Cf. A186434, A187452.
%K A271913 nonn
%O A271913 1,2
%A A271913 _N. J. A. Sloane_, Apr 24 2016
%E A271913 More terms from _Jean-François Alcover_, Sep 03 2018