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A331428 Divide each side of a triangle into 2*n-1 (n>=1) equal parts and trace the corresponding cevians, i.e., join every point, except for the first and last ones, with the opposite vertex. a(n) is the number of points at which three cevians meet.

%I A331428 #21 Feb 14 2020 18:43:54
%S A331428 0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,0,12,0,0,0,0,42,0,0,0,0,12,0,0,0,48,
%T A331428 6,0,0,0,0,6,12,0,0,0,6,0,0,12,0,0,0,24,0,0,90,0,0,0,0,0,12,12,0,0,0,
%U A331428 0,0,0,0,66,0,0,0,24,0,0,0,0,12,0,0,0,12,0
%N A331428 Divide each side of a triangle into 2*n-1 (n>=1) equal parts and trace the corresponding cevians, i.e., join every point, except for the first and last ones, with the opposite vertex. a(n) is the number of points at which three cevians meet.
%C A331428 A bisection of A331423.
%F A331428 a(n) = A331423(2*n-1).
%t A331428 CevIntersections[n_] := Length[Solve[(n - i)*(n - j)*(n - k) - i*j*k == 0 && 0 < i < n &&  0 < j < n && 0 < k < n, {i, j, k}, Integers]];
%t A331428 Map[CevIntersections[#] &, Range[1,51,2]]
%Y A331428 Cf. A331423, A331425.
%K A331428 nonn
%O A331428 1,8
%A A331428 _César Eliud Lozada_, Jan 16 2020