A362014 Number of distinct lines passing through exactly two points in a triangular grid of side n.

0, 0, 3, 6, 18, 39, 81, 141, 237, 369, 561, 801, 1119, 1521, 2043, 2667, 3429, 4329, 5415, 6675, 8163, 9879, 11877, 14127, 16695, 19593, 22881, 26523, 30591, 35085, 40089, 45591, 51681, 58359, 65715, 73701, 82389, 91791, 102015, 113007, 124875

Offset: 0

Author

Caleb Stanford, Apr 03 2023

Keywords

• nonn

References

• Samuel Dittmer, Hiram Golze, Grant Molnar, and Caleb Stanford, Puzzle and Proof: A Decade of Problems from the Utah Math Olympiad, CRC Press, 2025, p. 34.

Crossrefs

Cf. A234248, A244504 (lines which contain 2 or more points), A050534 (total number of pairs of points). Both are upper bounds.

Formula

a(n) = A244504(n) - A234248(n). - Andrew Howroyd, Apr 03 2023