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⇱ A186716 - OEIS

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A186716
Irregular triangle C(n,k): the number of connected k-regular graphs on n vertices having girth at least six.
12
1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 5, 0, 0, 1, 0, 0, 0, 1, 32, 0, 0, 1, 0, 0, 0, 1, 385, 0, 0, 1, 0, 0, 0, 1, 7574, 0, 0, 1, 0, 0, 0, 1, 181227, 1, 0, 0, 1, 0, 0, 0, 0, 1
OFFSET
1,53
COMMENTS
Other than the first two rows, each row begins with 0, 0, 1.
REFERENCES
M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146.
EXAMPLE
1;
0, 1;
0, 0;
0, 0;
0, 0;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1, 1;
0, 0, 1, 0;
0, 0, 1, 1;
0, 0, 1, 0;
0, 0, 1, 5;
0, 0, 1, 0;
0, 0, 1, 32;
0, 0, 1, 0;
0, 0, 1, 385;
0, 0, 1, 0;
0, 0, 1, 7574;
0, 0, 1, 0;
0, 0, 1, 181227, 1;
0, 0, 1, 0, 0;
0, 0, 1, 4624501, 1;
0, 0, 1, 0, 0;
0, 0, 1, 122090544, 4;
0, 0, 1, 0, 0;
0, 0, 1, 3328929954, 19;
0, 0, 1, 0, 0;
0, 0, 1, 93990692595, 1272;
0, 0, 1, 0, 25;
0, 0, 1, 2754222605376, 494031;
0, 0, 1, 0, 13504;
CROSSREFS
Connected k-regular simple graphs with girth at least 6: A186726 (any k), this sequence (triangle); specific k: A185116 (k=2), A014374 (k=3), A058348 (k=4).
Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth at least g: A068934 (g=3), A186714 (g=4), A186715 (g=5), this sequence (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).
Sequence in context: A048682 A375560 A375558 * A331039 A171915 A380270
KEYWORD
nonn,hard,tabf
AUTHOR
Jason Kimberley, Nov 23 2011
EXTENSIONS
C(36,3) from House of Graphs via Jason Kimberley, May 21 2017
STATUS
approved