A335102 Irregular triangle read by rows: consider the regular n-gon defined in A007678. T(n,k) (n >= 1, k >= 4+2*t where t>=0) is the number of non-boundary vertices in the n-gon at which k polygons meet.

0, 0, 0, 1, 5, 12, 1, 35, 40, 8, 1, 126, 140, 20, 0, 1, 330, 228, 60, 12, 0, 1, 715, 644, 112, 0, 0, 0, 1, 1365, 1168, 208, 0, 0, 0, 0, 1, 2380, 1512, 216, 54, 54, 0, 0, 0, 1, 3876, 3360, 480, 0, 0, 0, 0, 0, 0, 1, 5985, 5280, 660, 0, 0, 0, 0, 0, 0, 0, 1, 8855, 6144, 864, 264, 24, 0, 0, 0, 0, 0, 0, 12, 12650

Offset

1,5

Links

Table of n, a(n) for n=1..80.

Scott R. Shannon, Image of the vertices for n=5.

Scott R. Shannon, Image of the vertices for n=6.

Scott R. Shannon, Image of the vertices for n=8.

Scott R. Shannon, Image of the vertices for n=12.

Scott R. Shannon, Image of the vertices for n=13.

Scott R. Shannon, Image of the vertices for n=16.

Scott R. Shannon, Image of the vertices for n=18.

Scott R. Shannon, Image of the vertices for n=20.

Scott R. Shannon, Image of the vertices for n=24.

Scott R. Shannon, Image of the vertices for n=30.

Index entries for sequences related to stained glass windows

Formula

If n = 2t+1 is odd then the n-th row has a single term, T(2t+1, 2t+4) = binomial(2t+1,4) (these values are given in A053126).

The full leading column is A292104.

Row sums are given by A006561.

Example

Table begins:
0;
0;
0;
1;
5;
12, 1;
35;
40, 8, 1;
126;
140, 20, 0, 1;
330;
228, 60, 12, 0, 1;
715;
644, 112, 0, 0, 0, 1;
1365;
1168, 208, 0, 0, 0, 0, 1;
2380;
1512, 216, 54, 54, 0, 0, 0, 1;
3876;
3360, 480, 0, 0, 0, 0, 0, 0, 1;
5985;
5280, 660, 0, 0, 0, 0, 0, 0, 0, 1;
8855;
6144, 864, 264, 24, 0, 0, 0, 0, 0, 0, 1;
12650;
11284, 1196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
17550;
15680, 1568, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
23751;
13800, 2250, 420, 180, 120, 30, 0, 0, 0, 0, 0, 0, 0, 1;
31465;
28448, 2464, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
40920;
37264, 2992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
52360;

Crossrefs

Cf. A006561, A007569, A007678, A053126, A292104, A333275,

Sequence in context: A322153 A022835 A022834 * A342069 A046610 A009842

Adjacent sequences: A335099 A335100 A335101 * A335103 A335104 A335105

Keyword

nonn,tabf

Author

Scott R. Shannon and N. J. A. Sloane, May 23 2020

Status

approved