A367302 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 vertices in the resulting planar graph.

3, 6, 4, 22, 9, 5, 108, 69, 15, 6, 300, 345, 215, 25, 7, 919, 1337, 1285, 397, 49, 8, 1626, 2885, 4435, 2461, 1008, 65, 9, 3558, 7445, 11310, 7873, 5817, 1601, 144, 10, 5824, 12833, 24490, 21271, 19677, 9225, 3069, 181, 11, 9843, 23365, 46610, 46183, 49973, 33201, 17316, 4401, 352, 12

Offset

3,1

Comments

See A366483 and A367276 for other images of the n-gons.

Links

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

Scott R. Shannon, Image for T(5,5).

Scott R. Shannon, Image for T(8,3).

Scott R. Shannon, Image for T(12,2).

Formula

a(n,k) = A367305(n,k) - A367304(n,k) + 1 (Euler).

Example

The table begins:
3, 6, 22, 108, 300, 919, 1626, 3558, 5824, 9843, 14352, 23845, 30951, 47196, ...
4, 9, 69, 345, 1337, 2885, 7445, 12833, 23365, 36589, 64669, 80133, 138313, ...
5, 15, 215, 1285, 4435, 11310, 24490, 46610, 81005, 131560, 202610, 298690, ...
6, 25, 397, 2461, 7873, 21271, 46183, 87475, 150445, 249985, 388885, 569839, ...
7, 49, 1008, 5817, 19677, 49973, 106169, 200564, 346682, 560672, 861329, ...
8, 65, 1601, 9225, 33201, 83361, 182705, 341433, 597169, 961761, 1490689, ...
9, 144, 3069, 17316, 57555, 145062, 306684, 576783, 994230, 1605357, 2462112, ...
10, 181, 4401, 25201, 87301, 218211, 469401, 877291, 1522231, 2452231, 3781541, ...
11, 352, 7326, 40568, 133793, 335192, 706387, 1324851, 2279794, 3676431, ...
12, 325, 7897, 53125, 182713, 456253, 990229, 1849549, 3207325, 5171497, ...
13, 741, 14963, 81757, 267995, 668811, 1406366, 2632708, 4524910, ...
14, 785, 19489, 107157, 360389, 893117, 1896665, 3536387, 6103889, ...
15, 1395, 27420, 148335, 484005, 1204395, 2528445, 4726770, 8116650, ...
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Crossrefs

Cf. A367303 (internal vertices), A367304 (regions), A367305 (edges), A366483 (first row), A367276 (second row).

Sequence in context: A128719 A145691 A245767 * A009782 A294670 A016615

Adjacent sequences: A367299 A367300 A367301 * A367303 A367304 A367305

Keyword

nonn,tabl

Author

Scott R. Shannon, Nov 13 2023

Status

approved