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%I #16 Feb 22 2018 20:25:01
%S 1,1,1,1,0,1,1,1,1,0,1,1,1,1,1,1,0,1,0,1,1,2,2,1,1,0,2,0,0,1,1,3,6,2,
%T 1,1,0,3,0,2,0,1,1,5,23,12,1,1,1,0,5,0,31,0,0,1,1,7,112,220,7,1,1,1,0,
%U 8,0,1606,0,1,0,1,1,11,801,16829,388,9,1,1,1,0,12,0,193900,0,6,0,0,1,1,16,7840,2452820,406824,267,8,1,1,1,0,18,0,32670332,0,3727,0,0,0
%N Triangular array E(n,k) counting not necessarily connected k-regular simple graphs on n vertices with girth at least 4.
%C Row sums give A185314.
%H Jason Kimberley, <a href="/A185304/b185304.txt">Table of n, a(i)=E(n,k) for i = 1..139 (n = 1..22)</a>
%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 E(n,k) = A186714(n,k) + A185204(n,k).
%e 1: 1;
%e 2: 1, 1;
%e 3: 1, 0;
%e 4: 1, 1, 1;
%e 5: 1, 0, 1;
%e 6: 1, 1, 1, 1;
%e 7: 1, 0, 1, 0;
%e 8: 1, 1, 2, 2, 1;
%e 9: 1, 0, 2, 0, 0;
%e 10: 1, 1, 3, 6, 2, 1;
%e 11: 1, 0, 3, 0, 2, 0;
%e 12: 1, 1, 5, 23, 12, 1, 1;
%e 13: 1, 0, 5, 0, 31, 0, 0;
%e 14: 1, 1, 7, 112, 220, 7, 1, 1;
%e 15: 1, 0, 8, 0, 1606, 0, 1, 0;
%e 16: 1, 1, 11, 801, 16829, 388, 9, 1, 1;
%e 17: 1, 0, 12, 0, 193900, 0, 6, 0,0;
%e 18: 1, 1, 16, 7840, 2452820, 406824, 267, 8, 1, 1;
%e 19: 1, 0, 18, 0, 32670332, 0, 3727, 0,0, 0;
%e 20: 1, 1, 24, 97723, 456028489, 1125022326, 483012, 741, 13, 1, 1;
%e 21: 1, 0, 27, 0, 6636066134, 0, 69823723, 0, 1, 0, 0;
%e 22: 1, 1, 34, 1436873, 100135577994, 3813549359275, 14836130862, 2887493, ?, 14, 1;
%Y Not necessarily connected k-regular simple graphs with girth at least 4: A185314 (any k), this sequence (triangle); specified degree k: A008484 (k=2), A185334 (k=3), A185344 (k=4), A185354 (k=5), A185364 (k=6).
%K nonn,hard,tabf
%O 1,22
%A _Jason Kimberley_, Jan 19 2013
%E E(10,2) corrected by the author, Mar 26 2013
%E a(32)=E(10,2) in b-file corrected as above by _Andrew Howroyd_, Feb 22 2018
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