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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.
6
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
B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, arXiv:math/9508209 [math.MG]; some typos in the published version are corrected in the revisions from 2006.
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).
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
Columns give A292104, A101363 (2n-gon), A101364, A101365.
Row sums give A006561.
Sequence in context: A322153 A022835 A022834 * A342069 A046610 A009842
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved