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%I #47 Aug 17 2022 10:14:48
%S 1,6,4,19,32,11,30,96,90,24,61,188,316,246,50,78,332,580,672,462,80,
%T 127,460,1081,1476,1590,856,154,150,712,1510,2442,2982,2688,1476,220,
%U 217,916,2306,3528,5370,5504,4861,2420,375,246,1204,2930,5310,7742,9440,9288,7360,3630,444
%N Table read by antidiagonals: T(n,k) (n >= 3, k >= 1) is the number of regions 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="/A356044/a356044.jpg">Image of T(5,9) = 3961</a>.
%H Scott R. Shannon, <a href="/A356044/a356044_1.jpg">Image of T(6,8) = 7176</a>.
%H Scott R. Shannon, <a href="/A356044/a356044_2.jpg">Image of T(7,5) = 5370</a>.
%H Scott R. Shannon, <a href="/A356044/a356044_3.jpg">Image of T(8,4) = 5504</a>.
%H Scott R. Shannon, <a href="/A356044/a356044_4.jpg">Image of T(12,4) = 32532</a>.
%H Scott R. Shannon, <a href="/A356044/a356044_5.jpg">Image of T(14,6) = 160874</a>.
%H Scott R. Shannon, <a href="/A356044/a356044.txt">Table for n = 3..25</a>.
%F T(n,1) = A007678(n).
%F T(3,k) = A092098(k).
%F T(4,k) = A108914(k).
%e The table begins:
%e 1, 6, 19, 30, 61, 78, 127, 150, 217, 246,...
%e 4, 32, 96, 188, 332, 460, 712, 916, 1204, 1488,...
%e 11, 90, 316, 580, 1081, 1510, 2306, 2930, 3961, 4780,...
%e 24, 246, 672, 1476, 2442, 3528, 5310, 7176, 9072, 11352,...
%e 50, 462, 1590, 2982, 5370, 7742, 11390, 14742, 19650, 23982,...
%e 80, 856, 2688, 5504, 9440, 13968, 20216, 27008, 34888, 43792,...
%e 154, 1476, 4861, 9288, 16408, 23886, 34741, 45324, 59860, 73548,...
%e 220, 2420, 7360, 14980, 25480, 37690, 54180, 72280, 93400, 116970,...
%e 375, 3630, 11661, 22374, 39051, 57222, 82545, 108174, 142143, 175230,...
%e 444, 5400, 15864, 32532, 55500, 82032, 118056, 157236, 203148, 254184,...
%e 781, 7566, 23804, 45890, 79431, 116818, 167662, 220350, 288497, 356486,...
%e 952, 10668, 31682, 63700, 107184, 160874, 226996, 303324, 390950, 489860,...
%e 1456, 14070, 43546, 84270, 144976, 213720, 305656, 402510, 525586, 650550,...
%e 1696, 18832, 55792, 111840, 187776, 282000, 397072, 530432, 683616, 855920,...
%e 2500, 24072, 73645, 142732, 244410, 361012, 514795, 678912, 884800, 1096432,...
%e 2466, 30078, 91080, 181746, 306522, 458334, 647766, 864234, 1114668, 1394586,...
%e 4029, 38646, 117079, 227278, 387753, 573534, 816051, 1077414, 1401973, 1738918,...
%e .
%e .
%e See the attached text file for more examples and the cross references for further images.
%Y Cf. A007678 (first column), A092098 (first row), A108914 (second row).
%K nonn,tabl
%O 3,2
%A _Scott R. Shannon_, Jul 31 2022