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A367324
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 edges in the resulting planar graph.
2
3, 21, 8, 132, 92, 20, 429, 596, 290, 42, 1272, 1936, 2215, 708, 91, 2826, 6020, 7405, 4020, 1575, 136, 5640, 11088, 21150, 15120, 10962, 2632, 288, 10461, 26260, 43490, 38544, 35812, 17728, 5148, 390, 17094, 42144, 88230, 83136, 96257, 60672, 33291, 7800, 715
OFFSET
3,1
COMMENTS
See A367322, A367323 and the cross references for images of the n-gons.
FORMULA
T(n,k) = A367322(n,k) + A367323(n,k) - 1 (Euler).
EXAMPLE
The table begins:
3, 21, 132, 429, 1272, 2826, 5640, 10461, 17094, 26847, 41046, 61041, 84051, ...
8, 92, 596, 1936, 6020, 11088, 26260, 42144, 72296, 107832, 183340, 222940, ...
20, 290, 2215, 7405, 21150, 43490, 88230, 151135, 250825, 384360, 578840, ...
42, 708, 4020, 15120, 38544, 83136, 169686, 294678, 475500, 746340, 1140624, ...
91, 1575, 10962, 35812, 96257, 201054, 389991, 668458, 1096508, 1675835, ...
136, 2632, 17728, 60672, 163776, 341920, 673112, 1155144, 1892528, 2905088, ...
288, 5148, 33291, 108252, 283464, 591723, 1133928, 1941786, 3166605, 4837824, ...
390, 7800, 48870, 164470, 430840, 900890, 1735800, 2982660, 4849740, 7438490, ...
715, 12793, 79134, 255552, 660033, 1376870, 2619287, 4482654, 7284904, ...
756, 16512, 99348, 346140, 912960, 1894920, 3685056, 6313164, 10261200, ...
1508, 26806, 160641, 516932, 1322802, 2757339, 5221996, 8932664, 14483183, ...
1722, 35546, 210658, 696682, 1773828, 3718400, 7030464, 12067720, 19517596, ...
2835, 49995, 292590, 939720, 2388825, 4976130, 9394815, 16064970, 26003640, ...
3088, 63456, 370784, 1217664, 3081472, 6455872, 12162640, 20861328, 33700320, ...
4896, 85680, 493017, 1579436, 3995102, 8318525, 15667336, 26783636, ...
4320, 99036, 593784, 1958922, 4978872, 10395450, 19644408, ...
7923, 137693, 781470, 2499792, 6298633, 13109658, 24645983, ...
8360, 167160, 941940, 3068280, 7705420, 16112480, 30238400, ...
12180, 210378, 1180683, 3772692, 9476418, 19717089, ...
12782, 252296, 1400674, 4547884, 11375584, 23776236, ...
17963, 308591, 1716306, 5478232, 13725457, 28550084, ...
16344, 350448, 1981416, 6460080, 16185624, ...
25600, 437700, 2415825, 7704700, 19262750, ...
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CROSSREFS
Cf. A367322 (vertices), A367323 (regions), A274586 (1st row), A331448 (2nd row), A329710 (3rd row), A330845 (4th row), A333112 (5th row), A333110 (6th row), A332429 (7th row), A332419 (8th row), A135565 (1st column).
Sequence in context: A229197 A188721 A371102 * A212996 A089999 A124397
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved