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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 (list; graph; refs; listen; history; text; internal format)
 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. LINKS Jason Kimberley, Rows n = 1..37 of triangle, flattened House of Graphs, Cubic graphs Jason Kimberley, Connected regular graphs with girth at least 6 M. Meringer, Tables of Regular Graphs M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (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: A294393 A047754 A048682 * A331039 A171915 A287703 Adjacent sequences:  A186713 A186714 A186715 * A186717 A186718 A186719 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

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Last modified August 5 20:11 EDT 2021. Contains 346488 sequences. (Running on oeis4.)