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 A186715 Irregular triangle C(n,k)=number of connected k-regular graphs on n vertices having girth at least five. 15
 1, 0, 1, 0, 0, 0, 0, 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, 2, 0, 0, 1, 0, 0, 0, 1, 9, 0, 0, 1, 0, 0, 0, 1, 49, 0, 0, 1, 0, 0, 0, 1, 455, 0, 0, 1, 0, 1, 0, 0, 1, 5783, 2, 0, 0, 1, 0, 8, 0, 0, 1, 90938, 131, 0, 0, 1, 0, 3917, 0, 0, 1, 1620479, 123859 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,34 COMMENTS Brendan McKay has observed that C(26,3) = 31478584 is output by genreg, minibaum, and snarkhunter, but Meringer's table currently has C(26,3) = 31478582. - Jason Kimberley, May 19 2017 LINKS Jason Kimberley, Table of i, a(i) for i = 1..111 (n = 1..28) 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. [Jason Kimberley, Jan 29 2011] Jason Kimberley, Partial table of i, a(i) for i = 1..137 (n = 1..33) Jason Kimberley, Partial table of i, n, k, a(i)=C(n,k) for n = 1..33 Jason Kimberley, Connected regular graphs with girth at least 5 EXAMPLE 01: 1; 02: 0, 1; 03: 0, 0; 04: 0, 0; 05: 0, 0, 1; 06: 0, 0, 1; 07: 0, 0, 1; 08: 0, 0, 1; 09: 0, 0, 1; 10: 0, 0, 1, 1; 11: 0, 0, 1, 0; 12: 0, 0, 1, 2; 13: 0, 0, 1, 0; 14: 0, 0, 1, 9; 15: 0, 0, 1, 0; 16: 0, 0, 1, 49; 17: 0, 0, 1, 0; 18: 0, 0, 1, 455; 19: 0, 0, 1, 0, 1; 20: 0, 0, 1, 5783, 2; 21: 0, 0, 1, 0, 8; 22: 0, 0, 1, 90938, 131; 23: 0, 0, 1, 0, 3917; 24: 0, 0, 1, 1620479, 123859; 25: 0, 0, 1, 0, 4131991; 26: 0, 0, 1, 31478584, 132160608; 27: 0, 0, 1, 0, 4018022149; 28: 0, 0, 1, 656783890, 118369811960; CROSSREFS The row sums are given by A186725. Connected k-regular simple graphs with girth at least 5: A186725 (all k), this sequence (triangle); A185115 (k=2), A014372 (k=3), A058343 (k=4), A205295 (k=5). 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), this sequence (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). Sequence in context: A206499 A277885 A109527 * A219485 A057918 A242192 Adjacent sequences:  A186712 A186713 A186714 * A186716 A186717 A186718 KEYWORD nonn,hard,tabf AUTHOR Jason Kimberley, Oct 17 2011 STATUS approved

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Last modified October 21 14:48 EDT 2019. Contains 328301 sequences. (Running on oeis4.)