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A343870
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Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) planar graphs with n edges and k nodes (n >= 1, 2 <= k <= n + 1).
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3
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1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 3, 3, 1, 0, 0, 0, 0, 2, 9, 4, 1, 0, 0, 0, 0, 1, 13, 20, 6, 1, 0, 0, 0, 0, 0, 11, 49, 40, 7, 1, 0, 0, 0, 0, 0, 5, 77, 158, 70, 9, 1, 0, 0, 0, 0, 0, 2, 75, 406, 426, 121, 11, 1, 0, 0, 0, 0, 0, 0, 47, 662, 1645, 1018, 189, 13, 1, 0
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OFFSET
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1,19
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LINKS
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FORMULA
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T(n, n) = 1 for n >= 3.
T(n, n-1) = A253186(n-3) for n >= 3.
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EXAMPLE
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Triangle T(n,k) begins (n edges >= 1, k vertices >= 2):
1;
0, 0;
0, 1, 0;
0, 0, 1, 0;
0, 0, 1, 1, 0;
0, 0, 1, 2, 1, 0;
0, 0, 0, 3, 3, 1, 0;
0, 0, 0, 2, 9, 4, 1, 0;
0, 0, 0, 1, 13, 20, 6, 1, 0;
0, 0, 0, 0, 11, 49, 40, 7, 1, 0;
0, 0, 0, 0, 5, 77, 158, 70, 9, 1, 0;
0, 0, 0, 0, 2, 75, 406, 426, 121, 11, 1, 0;
...
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PROG
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(nauty) geng -C $k $n:$n | planarg -q | countg -q # Georg Grasegger, Jun 05 2023
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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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