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A341923
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Array read by antidiagonals: T(n,k) is the number of 3-connected triangulations of a disk up to orientation-preserving isomorphisms with n interior nodes and k nodes on the boundary, n >= 1, k >= 3.
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7
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1, 1, 1, 1, 2, 5, 1, 2, 10, 24, 1, 3, 16, 60, 133, 1, 3, 28, 122, 386, 846, 1, 4, 39, 242, 925, 2652, 5661, 1, 4, 58, 419, 2039, 7066, 18914, 39556, 1, 5, 78, 711, 4101, 17138, 54560, 139264, 286000, 1, 5, 106, 1128, 7801, 38166, 142802, 426462, 1048947, 2123329
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OFFSET
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1,5
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COMMENTS
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The initial terms of this sequence can also be computed using the tool "plantri", in particular the command "./plantri -u -v -o -P [n]" will compute values for a diagonal.
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..1275
G. Brinkmann and B. McKay, Plantri (program for generation of certain types of planar graph)
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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 | 5 10 16 28 39 58 ...
4 | 24 60 122 242 419 711 ...
5 | 133 386 925 2039 4101 7801 ...
6 | 846 2652 7066 17138 38166 79908 ...
7 | 5661 18914 54560 142802 345099 782210 ...
8 | 39556 139264 426462 1188412 3067938 7433635 ...
...
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PROG
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(PARI) A341923Array(8, 6) \\ See links in A342053 for program file.
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CROSSREFS
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Columns k=3..6 are A002709, A341924, A341925, A341926.
Antidiagonal sums are A342052.
Cf. A262586 (2-connected), A341856 (rooted), A342053 (unrooted).
Sequence in context: A004575 A021402 A201890 * A146097 A091953 A228824
Adjacent sequences: A341920 A341921 A341922 * A341924 A341925 A341926
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KEYWORD
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nonn,tabl
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AUTHOR
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Andrew Howroyd, Feb 26 2021
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STATUS
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approved
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