A329714 Irregular table read by rows: Take a heptagon with all diagonals drawn, as in A329713. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

35, 7, 7, 0, 1, 504, 224, 112, 28, 2331, 1883, 1008, 273, 92, 7, 7658, 6314, 3416, 798, 182, 28, 18662, 17514, 8463, 2898, 714, 175, 28, 7, 0, 0, 0, 1, 40404, 35462, 18508, 5796, 1330, 266, 28

Offset

1,1

Comments

See the links in A329713 for images of the heptagons.

Links

Lars Blomberg, Table of n, a(n) for n = 1..251 (the first 27 rows)

Example

A heptagon with no other points along its edges, n = 1, contains 35 triangles, 7 quadrilaterals, 7 pentagons, 1 heptagon and no other n-gons, so the first row is [35,7,7,0,1]. A heptagon with 1 point dividing its edges, n = 2, contains 504 triangles, 224 quadrilaterals, 112 pentagons, 28 hexagons and no other n-gons, so the second row is [504,224,112,28].
Triangle begins:
35, 7, 7, 0, 1;
504, 224, 112, 28;
2331, 1883, 1008, 273, 92, 7;
7658, 6314, 3416, 798, 182, 28;
18662, 17514, 8463, 2898, 714, 175, 28, 7, 0, 0, 0, 1;
40404, 35462, 18508, 5796, 1330, 266, 28;
73248, 71596, 35777, 11669, 2654, 651, 70, 49;
The row sums are A329713.

Crossrefs

Cf. A329713 (regions), A333112 (edges), A333113 (vertices), A331906, A007678, A092867, A331452.

Sequence in context: A272683 A366923 A037934 * A034086 A277079 A248477

Adjacent sequences: A329711 A329712 A329713 * A329715 A329716 A329717

Keyword

nonn,tabf

Author

Scott R. Shannon and N. J. A. Sloane, Mar 07 2020

Status

approved