A367305 - OEIS

A367305

Table read by antidiagonals: Place k equally spaced points on each side of a regular n-gon and join every pair of these n*k points by a chord; T(n,k) (n >= 3, k >= 0) gives the number of edges in the resulting planar graph.

3, 9, 4, 48, 16, 5, 237, 156, 30, 6, 684, 788, 460, 54, 7, 1962, 2880, 2660, 888, 105, 8, 3630, 6468, 9055, 5274, 2086, 152, 9, 7617, 15800, 23000, 16914, 11830, 3400, 306, 10, 12654, 27828, 49515, 44874, 39725, 19240, 6264, 410, 11, 21114, 49936, 93995, 96630, 100569, 67632, 34947, 9170, 737, 12

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

3,1

COMMENTS

See A367302, A367304, A366485, A367279 for images of the n-gons.

LINKS

Table of n, a(n) for n=3..57.

FORMULA

a(n,k) = A367302(n,k) + A367304(n,k) - 1 (Euler).

EXAMPLE

The table begins:

3, 9, 48, 237, 684, 1962, 3630, 7617, 12654, 21114, 31170, 50280, 66687, 99342, ...

4, 16, 156, 788, 2880, 6468, 15800, 27828, 49936, 78732, 134656, 173396, ...

5, 30, 460, 2660, 9055, 23000, 49515, 93995, 163100, 264635, 407325, 600550, ...

6, 54, 888, 5274, 16914, 44874, 96630, 182718, 314334, 518832, 804030, 1180314, ...

7, 105, 2086, 11830, 39725, 100569, 213339, 402479, 695240, 1124046, 1726305, ...

8, 152, 3400, 19240, 67632, 169720, 368560, 689408, 1201416, 1935944, 2993104, ...

9, 306, 6264, 34947, 115749, 291132, 614979, 1155708, 1991448, 3214809, ...

10, 410, 9170, 51670, 176460, 440940, 943520, 1764520, 3055110, 4922870, ...

11, 737, 14850, 81620, 268521, 671869, 1415139, 2652837, 4563944, 7358736, ...

12, 780, 17172, 109224, 370584, 924912, 1992528, 3723372, 6442428, 10386180, ...

13, 1534, 30212, 164203, 537303, 1339702, 2815995, 5269758, 9055800, ...

14, 1750, 39774, 217112, 723940, 1795290, 3801168, 7091406, 12223806, ...

15, 2865, 55230, 297600, 969765, 2411595, 5061195, 9459285, 16241160, ...

CROSSREFS

Cf. A367302 (vertices), A367303 (internal vertices), A367304 (regions), A366485 (first row), A367279 (second row).

Sequence in context: A180485 A370464 A357254 * A258580 A021966 A016675

Adjacent sequences: A367302 A367303 A367304 * A367306 A367307 A367308

KEYWORD

nonn,tabl

AUTHOR

Scott R. Shannon, Nov 13 2023

STATUS

approved