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Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 4.
16

%I #26 Nov 04 2013 04:03:30

%S 1,1,2,1,3,2,4,2,7,3,14,6,44,37,350,1616,18042,193919,2867779,

%T 32674078,1581632332,6705889886

%N Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 4.

%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/E_girth_ge_4">Not necessarily connected k-regular graphs with girth at least 4</a>

%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/E_k-reg_girth_ge_g_index">Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g</a>

%F a(n) = A186724(n) + A185214(n).

%F a(n) is the sum of the n-th row of A185304.

%Y Regular graphs, of any degree, with girth at least 4: A186724 (connected), A185214 (disconnected), this sequence (not-necessarily connected).

%Y Not necessarily connected k-regular simple graphs with girth at least 4: this sequence (any k), A185304 (triangle); specified degree k: A008484 (k=2), A185334 (k=3), A185344 (k=4), A185354 (k=5), A185364 (k=6).

%Y Not necessarily connected regular simple graphs with girth at least g: A005176 (g=3), this sequence (g=4), A185315 (g=5), A185316 (g=6), A185317 (g=7), A185318 (g=8), A185319 (g=9).

%K nonn,more,hard

%O 0,3

%A _Jason Kimberley_, May 23 2012