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%I #6 Jan 21 2013 08:45:24
%S 0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,1,0,0,2,0,0,0,2,2,1,0,0,3,0,1,0,0,4,8,
%T 3,1,0,0,5,0,8,0,0,0,6,29,25,3,1,0,0,9,0,88,0,1,0,0,10,138,377,66,5,1,
%U 0,0,13,0,2026,0,25,0,0,0,17,774,13349,8029,297,5,1,0,0,21,0,104593,0,8199,0,1,0,0,25,5678,930571,3484759,377004,1562,7,1
%N Triangular array D(n,k) counting disconnected k-regular simple graphs on n vertices with girth exactly 3.
%H Jason Kimberley, <a href="/A210703/b210703.txt">Table of i, a(i)=D(n,k) for i = 2..145 (n = 2..24)</a>
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/D_k-reg_girth_eq_g_index">Index of sequences counting disconnected k-regular simple graphs with girth exactly g</a>
%F D(n,k) = A068933(n,k) - A185204(n,k) [the former is padded to be a tabl but the latter is a tabf].
%F D(n,k) = A185643(n,k) - A186733(n,k) [both are tabl but the result is tabf].
%e 2: 0;
%e 3: 0;
%e 4: 0, 0;
%e 5: 0, 0;
%e 6: 0, 0, 1;
%e 7: 0, 0, 1;
%e 8: 0, 0, 1, 1;
%e 9: 0, 0, 2, 0;
%e 10: 0, 0, 2, 2, 1;
%e 11: 0, 0, 3, 0, 1;
%e 12: 0, 0, 4, 8, 3, 1;
%e 13: 0, 0, 5, 0, 8, 0;
%e 14: 0, 0, 6, 29, 25, 3, 1;
%e 15: 0, 0, 9, 0, 88, 0, 1;
%e 16: 0, 0, 10, 138, 377, 66, 5, 1;
%e 17: 0, 0, 13, 0, 2026, 0, 25, 0;
%e 18: 0, 0, 17, 774, 13349, 8029, 297, 5, 1;
%e 19: 0, 0, 21, 0, 104593, 0, 8199, 0, 1;
%e 20: 0, 0, 25, 5678, 930571, 3484759, 377004, 1562, 7, 1;
%e 21: 0, 0, 33, 0, 9124627, 0, 22014143, 0, 100, 0;
%e 22: 0, 0, 39, 53324, 96699740, 2595985769, 1493574756, 21617036, 10901, 9, 1;
%e 23: 0, 0, 49, 0, 1095467916, 0, 114880777582, 0, 3470736, 0, 1;
%e 24: 0, 0, 60, 622716, 13175254799, 2815099031409, 9919463450854, 733460349818, 1473822243, 88238, 11, 1;
%Y The sum of the n-th row is A210713(n).
%Y Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), this sequence (triangle); for a fixed k: A185033 (k=3), A185043 (k=4), A185053 (k=5), A185063 (k=6).
%K nonn,hard,tabf
%O 2,19
%A _Jason Kimberley_, Jan 21 2013
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