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 A186714 Triangular array C(n, k) = number of connected k-regular graphs, having girth at least 4, with n nodes, 0 <= k <= n div 2. 19
 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 6, 2, 1, 0, 0, 1, 0, 2, 0, 0, 0, 1, 22, 12, 1, 1, 0, 0, 1, 0, 31, 0, 0, 0, 0, 1, 110, 220, 7, 1, 1, 0, 0, 1, 0, 1606, 0, 1, 0, 0, 0, 1, 792, 16828, 388, 9, 1, 1, 0, 0, 1, 0, 193900, 0, 6, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,23 LINKS Jason Kimberley, Connected regular graphs with girth at least 4 EXAMPLE 01: 1; 02: 0,1; 03: 0,0; 04: 0,0,1; 05: 0,0,1; 06: 0,0,1,1; 07: 0,0,1,0; 08: 0,0,1,2,1; 09: 0,0,1,0,0; 10: 0,0,1,6,2,1; 11: 0,0,1,0,2,0; 12: 0,0,1,22,12,1,1; 13: 0,0,1,0,31,0,0; 14: 0,0,1,110,220,7,1,1; 15: 0,0,1,0,1606,0,1,0; 16: 0,0,1,792,16828,388,9,1,1; 17: 0,0,1,0,193900,0,6,0,0; 18: 0,0,1,7805,2452818,406824,267,8,1,1; 19: 0,0,1,0,32670330,0,3727,0,0,0; 20: 0,0,1,97546,456028474,1125022325,483012,741,13,1,1; 21: 0,0,1,0,6636066099,0,69823723,0,1,0,0; 22: 0,0,1,1435720,100135577747,3813549359274,14836130862,2887493,?,14,1,1; 23: 0,0,1,0,1582718912968,0,?,0,?,0,0; CROSSREFS The sum of the n-th row is A186724(n). Connected k-regular simple graphs with girth at least 4: A186724 (any k), this sequence (triangle); specified degree k: A185114 (k=2), A014371 (k=3), A033886 (k=4), A058275 (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9). Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth *at least* g: A068934 (g=3), this sequence (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). Sequence in context: A319080 A025435 A304685 * A160382 A081221 A280827 Adjacent sequences:  A186711 A186712 A186713 * A186715 A186716 A186717 KEYWORD nonn,tabf,hard AUTHOR Jason Kimberley, Sep to Dec 2011. STATUS approved

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Last modified December 6 04:14 EST 2019. Contains 329784 sequences. (Running on oeis4.)