A359656 Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square.

0, 1, 0, 4, 56, 40, 368, 300, 48, 12, 3376, 3408, 960, 96, 7536, 7524, 2240, 436, 8, 42048, 45112, 13912, 2868, 168, 28, 97720, 105980, 34496, 7020, 832, 52, 8, 267240, 290456, 100560, 20576, 2688, 160, 24, 461800, 509824, 174400, 36228, 4608, 324, 16, 1411272, 1594296, 569152, 126408, 16856, 1408, 104

Offset

1,4

Comments

The number of points internal to each edge is given by A005728(n) - 2.

See A359653 and A359654 for images of the square.

Links

Table of n, a(n) for n=1..53.

Example

The table begins:
0, 1;
0, 4;
56, 40;
368, 300, 48, 12;
3376, 3408, 960, 96;
7536, 7524, 2240, 436, 8;
42048, 45112, 13912, 2868, 168, 28;
97720, 105980, 34496, 7020, 832, 52, 8;
267240, 290456, 100560, 20576, 2688, 160, 24;
461800, 509824, 174400, 36228, 4608, 324, 16;
1411272, 1594296, 569152, 126408, 16856, 1408, 104;
2054616, 2300184, 830280, 184664, 24480, 2332, 128, 8;
5296752, 6001228, 2253456, 517564, 72888, 7532, 472, 4;
.
.

Crossrefs

Cf. A359653 (regions), A359654 (vertices), A359655 (edges), A005728, A358889, A358885, A355801, A358951, A006842, A006843.

Sequence in context: A054751 A189873 A358542 * A329459 A143650 A143649

Adjacent sequences: A359653 A359654 A359655 * A359657 A359658 A359659

Keyword

nonn,tabf

Author

Scott R. Shannon and N. J. A. Sloane, Jan 10 2023

Status

approved