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A068934
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Triangular array C(n, r) = number of connected r-regular graphs with n nodes, 0 <= r < n.
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23
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1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 2, 1, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 5, 6, 3, 1, 1, 0, 0, 1, 0, 16, 0, 4, 0, 1, 0, 0, 1, 19, 59, 60, 21, 5, 1, 1, 0, 0, 1, 0, 265, 0, 266, 0, 6, 0, 1, 0, 0, 1, 85, 1544, 7848, 7849, 1547, 94, 9, 1, 1, 0, 0, 1, 0, 10778, 0, 367860, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,19
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COMMENTS
| A graph is called r-regular if every node has exactly r edges. The numbers in this table were copied from the column sequences.
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LINKS
| Jason Kimberley, Rows 1..16 of A068934 triangle, flattened
Jason Kimberley, Connected regular graphs (with girth at least 3)
Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g
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FORMULA
| C(n, r) = A051031(n, r) - A068933(n, r).
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CROSSREFS
| Connected regular simple graphs: A005177 (any degree -- sum of rows), this sequence (triangular array), specified degree r (columns): A002851 (r=3), A006820 (r=4), A006821 (r=5), A006822 (r=6), A014377 (r=7), A014378 (r=8), A014381 (r=9), A014382 (r=10), A014384 (r=11).
Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth at least g: this sequence (g=3), A186714 (g=4), A186715 (g=5), A186716 (g=6), A186717 (g=7), A186718 (g=8), A186719 (g=9).
Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth exactly g: A186733 (g=3), A186734 (g=4), A186735 (g=5), A186736 (g=6), A186737 (g=7), A186738 (g=8), A186739 (g=9).
Sequence in context: A073779 A081227 A004610 * A035200 A198066 A141664
Adjacent sequences: A068931 A068932 A068933 * A068935 A068936 A068937
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KEYWORD
| nonn,tabl,hard
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AUTHOR
| David Wasserman (dwasserm(AT)earthlink.net), Mar 08 2002
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EXTENSIONS
| Edited by Jason Kimberley, Sep 23 2009, Nov 2011, and Jan 2012.
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