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

1,2

Comments

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

Links

Table of n, a(n) for n=1..38.

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.

Formula

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

Crossrefs

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

Sequence in context: A260955 A072368 A334881 * A355054 A116138 A227268

Adjacent sequences: A367659 A367660 A367661 * A367663 A367664 A367665

Keyword

nonn,look

Author

Scott R. Shannon, Nov 26 2023

Status

approved