A340614 Irregular table read by rows: Take a Reuleaux triangle with all diagonals drawn, as in A340639. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

1, 18, 6, 79, 51, 12, 3, 252, 192, 60, 6, 6, 576, 600, 168, 73, 15, 1170, 1380, 390, 126, 6, 12, 2248, 2589, 894, 288, 66, 18, 3, 4026, 4332, 1662, 480, 108, 30, 6426, 7182, 2988, 943, 189, 36, 9942, 11268, 4470, 1266, 300, 84, 0, 6, 14508, 16941, 7098, 2119, 435, 120, 6, 6

Offset

1,2

Comments

See A340639 for images of the regions and A340644 for images of the vertices.

Links

Table of n, a(n) for n=1..58.

Wikipedia, Reuleaux triangle.

Example

A Reuleaux triangle with 1 point dividing its edges, n = 2, contains 18 triangles, 6 quadrilaterals and no other n-gons, so the second row is [18, 6]. A Reuleaux triangle with 2 points dividing its edges, n = 3, contains 79 triangles, 51 quadrilaterals, 12 pentagons, 3 hexagons and no other n-gons, so the third row is [79, 51, 12, 3].
The table begins:
1;
18, 6;
79, 51, 12, 3;
252, 192, 60, 6, 6;
576, 600, 168, 73, 15;
1170, 1380, 390, 126, 6, 12;
2248, 2589, 894, 288, 66, 18, 3;
4026, 4332, 1662, 480, 108, 30;
6426, 7182, 2988, 943, 189, 36;
9942, 11268, 4470, 1266, 300, 84, 0, 6;
14508, 16941, 7098, 2119, 435, 120, 6, 6;
21234, 23598, 10194, 3090, 636, 132, 12, 6;
28881, 34086, 13935, 4528, 1041, 177, 24, 3;
39588, 45384, 19470, 5796, 1380, 198, 48;
52197, 60744, 26409, 7831, 1914, 366, 21, 15;
68646, 78492, 33810, 10668, 2358, 396, 60;
87642, 100701, 44670, 13942, 2931, 555, 66, 21, 6;
111084, 127290, 55818, 17082, 3912, 696, 132, 6;
138453, 158907, 70158, 22233, 4869, 1002, 87, 15, 0, 4;
171276, 194622, 87312, 26748, 6132, 846, 174, 6, 6;

Crossrefs

Cf. A340639 (regions), A340644 (vertices), A340613 (edges), A007678, A092867.

Sequence in context: A331932 A038642 A040311 * A221351 A078085 A069951

Adjacent sequences: A340611 A340612 A340613 * A340615 A340616 A340617

Keyword

nonn,tabf

Author

Scott R. Shannon and N. J. A. Sloane, Jan 14 2021

Status

approved