%I #20 Aug 18 2022 14:22:07
%S 3,7,5,21,25,10,25,81,61,19,63,157,285,205,42,67,301,476,541,358,57,
%T 129,381,1020,1327,1526,681,135,133,665,1311,2185,2682,2417,1234,171,
%U 219,821,2215,3067,5250,5073,4716,2131,341,223,1109,2666,4921,7246,8937,8623,6861,3169,313
%N Table read by antidiagonals: T(n,k) (n >= 3, k >= 1) is the number of vertices formed in a regular n-gon by straight line segments when connecting the n corner vertices to the points dividing the sides into k equal parts.
%H Scott R. Shannon, <a href="/A354544/a354544.png">Image of T(4,9) = 1109</a>.
%H Scott R. Shannon, <a href="/A354544/a354544_1.png">Image of T(5,7) = 2215</a>.
%H Scott R. Shannon, <a href="/A354544/a354544_2.png">Image of T(7,6) = 7246</a>.
%H Scott R. Shannon, <a href="/A354544/a354544_3.png">Image of T(10,3) = 6861</a>.
%H Scott R. Shannon, <a href="/A354544/a354544_4.png">Image of T(11,4) = 21143</a>.
%H Scott R. Shannon, <a href="/A354544/a354544.txt">Table for n=3..25</a>.
%F T(n,1) = A007569(n).
%F T(3,k) = A331782(k).
%F T(4,k) = A355949(k).
%e The table begins:
%e 3, 7, 21, 25, 63, 67, 129, 133, 219, 223,...
%e 5, 25, 81, 157, 301, 381, 665, 821, 1109, 1353,...
%e 10, 61, 285, 476, 1020, 1311, 2215, 2666, 3810, 4421,...
%e 19, 205, 541, 1327, 2185, 3067, 4921, 6739, 8401, 10507,...
%e 42, 358, 1526, 2682, 5250, 7246, 11214, 14050, 19418, 23094,...
%e 57, 681, 2417, 5073, 8937, 13089, 19473, 26049, 33769, 42497,...
%e 135, 1234, 4716, 8623, 16173, 22780, 34398, 43813, 59391, 71614,...
%e 171, 2131, 6861, 14271, 24731, 36161, 53071, 70751, 91761, 115001,...
%e 341, 3169, 11451, 21143, 38665, 55221, 81983, 105403, 141405, 171689,...
%e 313, 4837, 14653, 31009, 53989, 78589, 115909, 154105, 199777, 249961,...
%e 728, 6787, 23491, 43850, 78858, 113517, 166829, 215788, 287404, 350663,...
%e 771, 9927, 30479, 61951, 105155, 157851, 224043, 299727, 386807, 485367,...
%e 1380, 12856, 43080, 81136, 144180, 208636, 304500, 395536, 524040, 641656,...
%e 1393, 17633, 54001, 109265, 184785, 277745, 392737, 525169, 677729, 849249,...
%e 2397, 22288, 73066, 138177, 243355, 353686, 513264, 668815, 882793, 1083564,...
%e 1855, 27595, 88291, 177085, 302167, 450469, 641539, 855829, 1106119, 1384183,...
%e 3895, 36139, 116337, 220933, 386403, 563351, 814093, 1063393, 1399407, 1721059,...
%e .
%e .
%e See the attached text file for more examples and the cross references for further images.
%Y Cf. A356044 (number of regions), A007569 (first column), A331782 (first row), A355949 (second row).
%K nonn,tabl
%O 3,1
%A _Scott R. Shannon_, Aug 18 2022