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

0,1

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, ... .

Links

Table of n, a(n) for n=0..47.

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.

Crossrefs

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

Sequence in context: A290582 A346071 A076941 * A006779 A003208 A174313

Adjacent sequences: A357195 A357196 A357197 * A357199 A357200 A357201

Keyword

nonn

Author

Scott R. Shannon, Sep 17 2022

Status

approved