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

1,8

Comments

A bisection of A331423.

Links

Table of n, a(n) for n=1..82.

Formula

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

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]]

Crossrefs

Cf. A331423, A331425.

Sequence in context: A341882 A307382 A339629 * A323487 A173453 A340979

Adjacent sequences: A331425 A331426 A331427 * A331429 A331430 A331431

Keyword

nonn

Author

César Eliud Lozada, Jan 16 2020

Status

approved