A367322 Table read by antidiagonals: Place k equally spaced points on each side of a regular n-gon and join every pair of the n*(k+1) boundary points by a chord; T(n,k) (n >= 3, k >= 0) gives the number of vertices in the resulting planar graph.

3, 10, 5, 58, 37, 10, 178, 257, 121, 19, 558, 817, 1055, 301, 42, 1255, 2757, 3506, 1753, 708, 57, 2532, 4825, 10410, 6913, 5369, 1145, 135, 4786, 12293, 21111, 17713, 17417, 8417, 2395, 171, 7804, 19241, 43740, 38497, 47796, 29121, 16434, 3581, 341

Offset

3,1

Comments

See A367323 and the cross references for further images of the n-gons.

Links

Table of n, a(n) for n=3..47.

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

Scott R. Shannon, Image for T(23,1).

Formula

T(n,k) = A367324(n,k) - A367323(n,k) + 1 (Euler).

Example

The table begins:
3, 10, 58, 178, 558, 1255, 2532, 4786, 7804, 12292, 18966, 28540, 39117, 56107, ...
5, 37, 257, 817, 2757, 4825, 12293, 19241, 33549, 49577, 87685, 101981, 178465, ...
10, 121, 1055, 3506, 10410, 21111, 43740, 74526, 124490, 190291, 288190, ...
19, 301, 1753, 6913, 17713, 38497, 80473, 139927, 225595, 356329, 549967, ...
42, 708, 5369, 17417, 47796, 99261, 194278, 331955, 546805, 833946, 1245314, ...
57, 1145, 8417, 29121, 80345, 167105, 333297, 570969, 939113, 1441153, 2153937, ...
135, 2395, 16434, 53155, 141147, 293374, 565767, 966493, 1580940, 2411533, ...
171, 3581, 23651, 80191, 213041, 444251, 862711, 1481141, 2413721, 3701951, ...
341, 6062, 39248, 126061, 329131, 684223, 1307845, 2233815, 3639020, 5549952, ...
313, 7513, 47293, 167941, 450457, 931345, 1830625, 3132349, 5103589, 7825201, ...
728, 12845, 79859, 255711, 660140, 1372008, 2608476, 4454477, 7236853, ...
771, 16871, 103517, 343855, 881959, 1847525, 3504971, 6013953, 9739227, ...
1380, 24136, 145635, 465721, 1192710, 2478121, 4694040, 8014891, 12995535, ...
1393, 30305, 182785, 602337, 1533681, 3211873, 6067041, 10402769, 16824161, ...
2397, 41583, 245684, 783803, 1995341, 4145230, 7829333, 13366897, ...
1855, 46801, 291637, 967123, 2476873, 5166055, 9798175, ...
3895, 67090, 389690, 1241765, 3146533, 6535659, 12317567, ...
3861, 80921, 466141, 1522001, 3840181, 8027441, 15094521, ...
6006, 102817, 589029, 1875511, 4734786, 9833104, ...
5963, 122849, 694387, 2259005, 5671887, 11852105, ...
8878, 151180, 856589, 2725041, 6858600, 14242153, ...
7321, 169297, 979777, 3205921, 8068321, ...
12675, 214851, 1206050, 3834451, 9626475, ...
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Crossrefs

Cf. A367323 (regions), A367324 (edges), A274585 (1st row), A331449 (2nd row), A330847 (3rd row), A330846 (4th row), A333113 (5th row), A333109 (6th row), A332428 (7th row), A332418 (8th row), A007569 (1st column).

Sequence in context: A281220 A280529 A281279 * A068489 A088337 A195919

Adjacent sequences: A367319 A367320 A367321 * A367323 A367324 A367325

Keyword

nonn,tabl

Author

Scott R. Shannon and N. J. A. Sloane, Nov 14 2023

Status

approved