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A342053
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Array read by antidiagonals: T(n,k) is the number of unrooted 3-connected triangulations of a disk with n interior nodes and k nodes on the boundary, n >= 1, k >= 3.
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8
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1, 1, 1, 1, 2, 4, 1, 2, 8, 16, 1, 3, 12, 38, 78, 1, 3, 20, 73, 219, 457, 1, 4, 27, 140, 503, 1404, 2938, 1, 4, 39, 235, 1089, 3661, 9714, 20118, 1, 5, 51, 392, 2149, 8796, 27715, 70454, 144113, 1, 5, 68, 610, 4050, 19419, 72204, 214664, 527235, 1065328
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OFFSET
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1,5
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COMMENTS
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For k >= 4, T(n,k) is the number of polyhedra with n+k vertices whose faces are all triangular, except one which is k-gonal.
The initial terms of this sequence can also be computed using the tool "plantri", in particular the command "./plantri -u -v -P [n]" will compute values for a diagonal.
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LINKS
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EXAMPLE
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Array begins:
===================================================
n\k | 3 4 5 6 7 8
----+----------------------------------------------
1 | 1 1 1 1 1 1 ...
2 | 1 2 2 3 3 4 ...
3 | 4 8 12 20 27 39 ...
4 | 16 38 73 140 235 392 ...
5 | 78 219 503 1089 2149 4050 ...
6 | 457 1404 3661 8796 19419 40485 ....
7 | 2938 9714 27715 72204 173779 393123 ...
8 | 20118 70454 214664 596906 1538221 3723976 ...
...
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PROG
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(PARI) A342053Array(8, 6) \\ See links for program.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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