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A368816
Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, in a regular 2n-gon when all vertices are connect by straight lines except for the n lines joining diametrically opposite vertices.
4
0, 0, 1, 12, 0, 0, 1, 40, 8, 8, 0, 0, 1, 100, 40, 20, 10, 0, 0, 0, 1, 204, 132, 12, 12, 0, 0, 0, 0, 0, 1, 378, 280, 126, 28, 0, 0, 0, 0, 0, 0, 0, 1, 688, 528, 176, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1188, 864, 72, 54, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
OFFSET
1,4
COMMENTS
See A368813 and A368814 for other images of the 2n-gons.
LINKS
FORMULA
Sum of row n = A368813(n).
EXAMPLE
The table begins:
0;
0, 1;
12, 0, 0, 1;
40, 8, 8, 0, 0, 1;
100, 40, 20, 10, 0, 0, 0, 1;
204, 132, 12, 12, 0, 0, 0, 0, 0, 1;
378, 280, 126, 28, 0, 0, 0, 0, 0, 0, 0, 1;
688, 528, 176, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
1188, 864, 72, 54, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
1840, 1360, 620, 220, 20, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
2508, 2552, 880, 198, 44, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
3648, 3576, 864, 216, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
.
.
CROSSREFS
Cf. A368813 (regions), A368814 (vertices), A368815 (edges), A368755, A368758.
Sequence in context: A242240 A225341 A369349 * A004012 A360223 A270256
KEYWORD
nonn,tabf
AUTHOR
Scott R. Shannon, Jan 06 2024
STATUS
approved