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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
OFFSET
1,23
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 A336352 A081221
KEYWORD
nonn,tabf,hard
AUTHOR
Jason Kimberley, Sep to Dec 2011.
STATUS
approved