A356044 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.

1, 6, 4, 19, 32, 11, 30, 96, 90, 24, 61, 188, 316, 246, 50, 78, 332, 580, 672, 462, 80, 127, 460, 1081, 1476, 1590, 856, 154, 150, 712, 1510, 2442, 2982, 2688, 1476, 220, 217, 916, 2306, 3528, 5370, 5504, 4861, 2420, 375, 246, 1204, 2930, 5310, 7742, 9440, 9288, 7360, 3630, 444

Offset

3,2

Links

Table of n, a(n) for n=3..57.

Scott R. Shannon, Image of T(5,9) = 3961.

Scott R. Shannon, Image of T(6,8) = 7176.

Scott R. Shannon, Image of T(7,5) = 5370.

Scott R. Shannon, Image of T(8,4) = 5504.

Scott R. Shannon, Image of T(12,4) = 32532.

Scott R. Shannon, Image of T(14,6) = 160874.

Scott R. Shannon, Table for n = 3..25.

Formula

T(n,1) = A007678(n).

T(3,k) = A092098(k).

T(4,k) = A108914(k).

Example

The table begins:
1,    6,     19,     30,     61,     78,     127,    150,     217,     246,...
4,    32,    96,     188,    332,    460,    712,    916,     1204,    1488,...
11,   90,    316,    580,    1081,   1510,   2306,   2930,    3961,    4780,...
24,   246,   672,    1476,   2442,   3528,   5310,   7176,    9072,    11352,...
50,   462,   1590,   2982,   5370,   7742,   11390,  14742,   19650,   23982,...
80,   856,   2688,   5504,   9440,   13968,  20216,  27008,   34888,   43792,...
154,  1476,  4861,   9288,   16408,  23886,  34741,  45324,   59860,   73548,...
220,  2420,  7360,   14980,  25480,  37690,  54180,  72280,   93400,   116970,...
375,  3630,  11661,  22374,  39051,  57222,  82545,  108174,  142143,  175230,...
444,  5400,  15864,  32532,  55500,  82032,  118056, 157236,  203148,  254184,...
781,  7566,  23804,  45890,  79431,  116818, 167662, 220350,  288497,  356486,...
952,  10668, 31682,  63700,  107184, 160874, 226996, 303324,  390950,  489860,...
1456, 14070, 43546,  84270,  144976, 213720, 305656, 402510,  525586,  650550,...
1696, 18832, 55792,  111840, 187776, 282000, 397072, 530432,  683616,  855920,...
2500, 24072, 73645,  142732, 244410, 361012, 514795, 678912,  884800,  1096432,...
2466, 30078, 91080,  181746, 306522, 458334, 647766, 864234,  1114668, 1394586,...
4029, 38646, 117079, 227278, 387753, 573534, 816051, 1077414, 1401973, 1738918,...
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See the attached text file for more examples and the cross references for further images.

Crossrefs

Cf. A007678 (first column), A092098 (first row), A108914 (second row).

Sequence in context: A180495 A213761 A160248 * A317858 A212891 A107983

Adjacent sequences: A356041 A356042 A356043 * A356045 A356046 A356047

Keyword

nonn,tabl

Author

Scott R. Shannon, Jul 31 2022

Status

approved