A367662 Number of regions formed in a hexagon by straight line segments when connecting the n-1 points between each corner that divide each edge into n equal parts to the n-1 points on the edge on the opposite side of the hexagon.

1, 6, 54, 252, 780, 1968, 4146, 7662, 13014, 21078, 32562, 46818, 67962, 93048, 123684, 166794, 217380, 271056, 349932, 428250, 523272, 645744, 784794, 918606, 1104966, 1304250, 1515018, 1768974, 2071662, 2317602, 2734242, 3101670, 3486990, 3987774, 4460862, 4978530, 5688804, 6316332

Offset: 1

Author

Scott R. Shannon, Nov 26 2023

Keywords

• nonn
• look

Comments

Keyword "look" is because of the linked images. - N. J. A. Sloane, Dec 01 2023

Links

• Scott R. Shannon, Image for n = 2.
• Scott R. Shannon, Image for n = 3.
• Scott R. Shannon, Image for n = 5.
• Scott R. Shannon, Image for n = 8.
• Scott R. Shannon, Image for n = 12.

Crossrefs

Cf. A367663 (vertices), A367664 (edges), A367665 (k-gons), A355798.

Formula

a(n) = A367664(n) - A367663(n) + 1 by Euler's formula.