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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
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
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
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved