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A049334
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Triangle read by rows: T(n, k) is the number of unlabeled connected planar simple graphs with n >= 1 nodes and 0<=k<=3*n-6 edges.
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10
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1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 2, 2, 1, 1, 0, 0, 0, 0, 3, 5, 5, 4, 2, 1, 0, 0, 0, 0, 0, 6, 13, 19, 22, 19, 13, 5, 2, 0, 0, 0, 0, 0, 0, 11, 33, 67, 107, 130, 130, 96, 51, 16, 5, 0, 0, 0, 0, 0, 0, 0, 23, 89, 236, 486, 804, 1112, 1211, 1026, 626, 275, 72, 14, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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1,11
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COMMENTS
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Planar graphs with n >= 3 nodes have at most 3*n-6 edges.
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LINKS
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FORMULA
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log(1 + B(x, y)) = Sum{n>0} A(x^n, y^n) / n where A(x, y) = Sum_{n>0, k>=0} T(n,k) * x^n * y^k and similarly B(x, y) with A039735. - Michael Somos, Aug 23 2015
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EXAMPLE
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n\k 0 1 2 3 4 5 6 7 8 9 10 11 12
--:-- -- -- -- -- -- -- -- -- -- -- -- --
1: 1
2: 0 1
3: 0 0 1 1
4: 0 0 0 2 2 1 1
5: 0 0 0 0 3 5 5 4 2 1
6: 0 0 0 0 0 6 13 19 22 19 13 5 2
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PROG
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(nauty) geng -c $n $k:$k | planarg -q | countg -q # Georg Grasegger, Jul 11 2023
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CROSSREFS
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KEYWORD
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nonn,tabf,nice
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AUTHOR
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STATUS
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approved
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