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A367323
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 regions in the resulting planar graph.
3
1, 12, 4, 75, 56, 11, 252, 340, 170, 24, 715, 1120, 1161, 408, 50, 1572, 3264, 3900, 2268, 868, 80, 3109, 6264, 10741, 8208, 5594, 1488, 154, 5676, 13968, 22380, 20832, 18396, 9312, 2754, 220, 9291, 22904, 44491, 44640, 48462, 31552, 16858, 4220, 375
OFFSET
3,2
COMMENTS
See A367322 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) - A367322(n,k) + 1 (Euler).
EXAMPLE
The table begins:
1, 12, 75, 252, 715, 1572, 3109, 5676, 9291, 14556, 22081, 32502, 44935, 62868, ...
4, 56, 340, 1120, 3264, 6264, 13968, 22904, 38748, 58256, 95656, 120960, ...
11, 170, 1161, 3900, 10741, 22380, 44491, 76610, 126336, 194070, 290651, ...
24, 408, 2268, 8208, 20832, 44640, 89214, 154752, 249906, 390012, 590658, ...
50, 868, 5594, 18396, 48462, 101794, 195714, 336504, 549704, 841890, 1249676, ...
80, 1488, 9312, 31552, 83432, 174816, 339816, 584176, 953416, 1463936, 2173976, ...
154, 2754, 16858, 55098, 142318, 298350, 568162, 975294, 1585666, 2426292, ...
220, 4220, 25220, 84280, 217800, 456640, 873090, 1501520, 2436020, 3736540, ...
375, 6732, 39887, 129492, 330903, 692648, 1311443, 2248840, 3645885, 5574756, ...
444, 9000, 52056, 178200, 462504, 963576, 1854432, 3180816, 5157612, 7906080, ...
781, 13962, 80783, 261222, 662663, 1385332, 2613521, 4478188, 7246331, ...
952, 18676, 107142, 352828, 891870, 1870876, 3525494, 6053768, 9778370, ...
1456, 25860, 146956, 474000, 1196116, 2498010, 4700776, 8050080, 13008106, ...
1696, 33152, 188000, 615328, 1547792, 3244000, 6095600, 10458560, 16876160, ...
2500, 44098, 247334, 795634, 1999762, 4173296, 7838004, 13416740, ...
2466, 52236, 302148, 991800, 2502000, 5229396, 9846234, ...
4029, 70604, 391781, 1258028, 3152101, 6574000, 12328417, ...
4500, 86240, 475800, 1546280, 3865240, 8085040, 15143880, ...
6175, 107562, 591655, 1897182, 4741633, 9883986, ...
6820, 129448, 706288, 2288880, 5703698, 11924132, ...
9086, 157412, 859718, 2753192, 6866858, 14307932, ...
9024, 181152, 1001640, 3254160, 8117304, ...
12926, 222850, 1209776, 3870250, 9636276, ...
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CROSSREFS
Cf. A367322 (vertices), A367324 (edges), A092867 (1st row), A255011 (2nd row), A331929 (3rd row), A331931 (4th row), A329713 (5th row), A333075 (6th row), A332421 (7th row), A333139 (8th row), A007678 (1st column).
Sequence in context: A166206 A040137 A092237 * A081987 A327972 A047709
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved