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.

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, 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, 0, 0, 0, 0, 66, 0, 0, 0, 24, 0, 0, 0, 0, 12, 0, 0, 0, 12, 0

Offset: 1

Author

César Eliud Lozada, Jan 16 2020

Keywords

• nonn

Comments

A bisection of A331423.

Crossrefs

Cf. A331423, A331425.

Programs

Mathematica

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]];
Map[CevIntersections[#] &, Range[1,51,2]]

Formula

a(n) = A331423(2*n-1).