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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.
4
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
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
KEYWORD
nonn,tabl
AUTHOR
Scott R. Shannon, Nov 13 2023
STATUS
approved