A331425 Divide each side of a triangle into 2*n (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.

1, 7, 13, 19, 25, 31, 37, 43, 49, 61, 61, 91, 73, 79, 91, 91, 97, 103, 109, 133, 133, 127, 133, 187, 145, 151, 157, 175, 169, 235, 181, 187, 205, 199, 229, 283, 217, 223, 235, 325, 241, 283, 253, 271, 331, 271, 277, 343, 289, 301, 301, 319, 313, 319, 349, 439

Offset

1,2

Comments

A bisection of A331423.

Links

Table of n, a(n) for n=1..56.

Formula

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

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[2, 50, 2]]

Crossrefs

Cf. A331423, A331428.

Sequence in context: A070419 A080199 A016921 * A260682 A354936 A348932

Adjacent sequences: A331422 A331423 A331424 * A331426 A331427 A331428

Keyword

nonn

Author

César Eliud Lozada, Jan 16 2020

Status

approved