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 A210703 Triangular array D(n,k) counting disconnected k-regular simple graphs on n vertices with girth exactly 3. 7
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,19 LINKS Jason Kimberley, Table of i, a(i)=D(n,k) for i = 2..145 (n = 2..24) FORMULA D(n,k) = A068933(n,k) - A185204(n,k) [the former is padded to be a tabl but the latter is a tabf]. D(n,k) = A185643(n,k) - A186733(n,k) [both are tabl but the result is tabf]. EXAMPLE 2: 0; 3: 0; 4: 0, 0; 5: 0, 0; 6: 0, 0, 1; 7: 0, 0, 1; 8: 0, 0, 1, 1; 9: 0, 0, 2, 0; 10: 0, 0, 2, 2, 1; 11: 0, 0, 3, 0, 1; 12: 0, 0, 4, 8, 3, 1; 13: 0, 0, 5, 0, 8, 0; 14: 0, 0, 6, 29, 25, 3, 1; 15: 0, 0, 9, 0, 88, 0, 1; 16: 0, 0, 10, 138, 377, 66, 5, 1; 17: 0, 0, 13, 0, 2026, 0, 25, 0; 18: 0, 0, 17, 774, 13349, 8029, 297, 5, 1; 19: 0, 0, 21, 0, 104593, 0, 8199, 0, 1; 20: 0, 0, 25, 5678, 930571, 3484759, 377004, 1562, 7, 1; 21: 0, 0, 33, 0, 9124627, 0, 22014143, 0, 100, 0; 22: 0, 0, 39, 53324, 96699740, 2595985769, 1493574756, 21617036, 10901, 9, 1; 23: 0, 0, 49, 0, 1095467916, 0, 114880777582, 0, 3470736, 0, 1; 24: 0, 0, 60, 622716, 13175254799, 2815099031409, 9919463450854, 733460349818, 1473822243, 88238, 11, 1; CROSSREFS The sum of the n-th row is A210713(n). 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). Sequence in context: A216228 A291957 A143063 * A275964 A284272 A175070 Adjacent sequences:  A210700 A210701 A210702 * A210704 A210705 A210706 KEYWORD nonn,hard,tabf AUTHOR Jason Kimberley, Jan 21 2013 STATUS approved

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Last modified May 19 10:36 EDT 2019. Contains 323390 sequences. (Running on oeis4.)