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%I #19 Mar 03 2024 22:23:09
%S 0,24,108,248,444,672,932,1204,1512,1836,2188,2548,2936,3332,3756,
%T 4192,4656,5128,5628,6136,6672,7216,7788,8368,8976,9592,10236,10888,
%U 11568,12256,12972,13696,14448,15208,15996,16792
%N Number of ways to choose three distinct points from a 5 X n grid so that they form an isosceles triangle.
%H 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 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, -2, 1).
%F Conjectured g.f.: 4*x* (x^16-x^14+2*x^10+2*x^9-x^8-x^7 + 5*x^6+6*x^5+6*x^4+x^3-8*x^2-15*x-6) /((x+1)*(x-1)^3).
%F Conjectured recurrence: a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n > 18.
%F The conjectured g.f. and recurrence are true. See paper in links. - _Chai Wah Wu_, May 07 2016
%t Join[{0, 24, 108, 248, 444, 672, 932, 1204, 1512, 1836, 2188, 2548, 2936, 3332}, LinearRecurrence[{2, 0, -2, 1}, {3756, 4192, 4656, 5128}, 20]] (* _Jean-François Alcover_, Sep 03 2018 *)
%Y Row 5 of A271910.
%Y Cf. A186434, A187452.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Apr 24 2016
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