A367324 - OEIS

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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.

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 (list; table; graph; refs; listen; history; text; internal format)

	OFFSET	`3,1`
	COMMENTS	`See A367322, A367323 and the cross references for images of the n-gons.`
	LINKS	`Table of n, a(n) for n=3..47.`
	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, ...` `.` `.` `.`
	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` `Adjacent sequences: A367321 A367322 A367323 * A367325 A367326 A367327`
	KEYWORD	`nonn,tabl`
	AUTHOR	`Scott R. Shannon and N. J. A. Sloane, Nov 14 2023`
	STATUS	`approved`

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Last modified July 9 00:53 EDT 2024. Contains 374171 sequences. (Running on oeis4.)