A333076 Irregular table read by rows: Take an octagon with all diagonals drawn, as in A333075. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

56, 24, 800, 608, 64, 16, 4136, 3400, 1272, 464, 40, 13840, 10800, 5296, 1264, 288, 64, 33160, 30048, 14744, 4456, 840, 152, 32, 70832, 62208, 30848, 8656, 1936, 288, 48, 129624, 124224, 61560, 19312, 4168, 840, 64, 16, 0, 8, 225200, 210608, 107552, 32768

Offset

1,1

Comments

See the links in A333075 for images of the octagons.

Links

Lars Blomberg, Table of n, a(n) for n = 1..207

Example

An octagon with no other points along its edges, n = 1, contains 56 triangles, 24 quadrilaterals and no other n-gons, so the first row is [56,24]. An octagon with 1 point dividing its edges, n = 2, contains 800 triangles, 608 quadrilaterals, 64 pentagons, 16 hexagons and no other n-gons, so the second row is [800,608,64,16].
Table begins:
56,24;
800,608,64,16;
4136,3400,1272,464,40;
13840,10800,5296,1264,288,64;
33160,30048,14744,4456,840,152,32;
70832,62208,30848,8656,1936,288,48;
The rows sums are A333075.

Crossrefs

Cf. A333075 (regions), A333109 (vertices), A333110 (edges), A331931, A331906, A007678, A092867, A331452.

Sequence in context: A005932 A109737 A092077 * A033376 A300449 A224343

Adjacent sequences: A333073 A333074 A333075 * A333077 A333078 A333079

Keyword

nonn,tabf

Author

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

Extensions

a(32) and beyond from Lars Blomberg, May 14 2020

Status

approved