A367662 - OEIS

%I #14 Dec 01 2023 20:43:07

%S 1,6,54,252,780,1968,4146,7662,13014,21078,32562,46818,67962,93048,

%T 123684,166794,217380,271056,349932,428250,523272,645744,784794,

%U 918606,1104966,1304250,1515018,1768974,2071662,2317602,2734242,3101670,3486990,3987774,4460862,4978530,5688804,6316332

%N 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.

%C Keyword "look" is because of the linked images. - _N. J. A. Sloane_, Dec 01 2023

%H Scott R. Shannon, <a href="/A367662/a367662.png">Image for n = 2</a>.

%H Scott R. Shannon, <a href="/A367662/a367662_1.png">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A367662/a367662_2.png">Image for n = 5</a>.

%H Scott R. Shannon, <a href="/A367662/a367662_3.png">Image for n = 8</a>.

%H Scott R. Shannon, <a href="/A367662/a367662_4.png">Image for n = 12</a>.

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

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

%K nonn,look

%O 1,2

%A _Scott R. Shannon_, Nov 26 2023