A357198 Number of edges in a hexagon when n internal hexagons are drawn between the 6n points that divide each side into n+1 equal parts.

6, 18, 54, 114, 198, 306, 438, 594, 774, 942, 1206, 1422, 1734, 2034, 2310, 2706, 3078, 3474, 3894, 4242, 4806, 5298, 5814, 6186, 6918, 7506, 8118, 8706, 9414, 9978, 10806, 11538, 12258, 13074, 13842, 14562, 15558, 16434, 17298, 17970, 19206, 20082, 21174, 22122, 23154, 24306, 25398, 26286

Offset: 0

Author

Scott R. Shannon, Sep 17 2022

Keywords

• nonn

Comments

Unlike similar dissections of the triangle and square, see A357008 and A357061, there is no obvious pattern for n values that yield hexagons with non-simple intersections; these n values begin 9, 11, 14, 19, 23, 27, 29, 32, 34, 35, 38, 39, 41, 43, ... .

Crossrefs

Cf. A357196 (regions), A357197 (vertices), A330845, A357008 (triangle), A357061 (square).

Formula

a(n) = A357196(n) + A357197(n) - 1 by Euler's formula.

Conjecture: a(n) = 12*n^2 + 6 for hexagons that only contain simple intersections when cut by n internal hexagons.