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A321304
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Triangle T(n,f): the number of bicolored connected cubic graphs on 2n vertices with f vertices of the first color.
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7
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1, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 5, 5, 5, 2, 2, 5, 10, 31, 46, 63, 46, 31, 10, 5, 19, 64, 248, 542, 931, 1052, 931, 542, 248, 64, 19, 85, 490, 2382, 7011, 15199, 23405, 27336, 23405, 15199, 7011, 2382, 490, 85, 509, 4595, 27233, 101002, 268675, 523246, 776657, 882321, 776657, 523246, 268675, 101002, 27233, 4595, 509
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OFFSET
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0,10
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COMMENTS
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These are connected, undirected, simple cubic graphs where each vertex has either the first or the second color. Row n has 2n+1 entries, 0<=f<=2n. The column f=0 (1, 0, 2, 5,...) counts the cubic graphs (A002851). The column f=1 (0, 1, 2, 10, 64, 490...) counts the rooted cubic graphs.
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LINKS
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FORMULA
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T(n,f) = T(n,2n-f).
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EXAMPLE
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The triangle starts:
0 vertices: 1;
2 vertices: 0, 0, 0;
4 vertices: 1, 1, 1, 1, 1;
6 vertices: 2, 2, 5, 5, 5, 2, 2;
8 vertices: 5, 10, 31, 46, 63, 46, 31, 10, 5;
10 vertices: 19, 64, 248, 542, 931, 1052, 931, 542, 248, 64, 19;
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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