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 A185643 Triangular array E(n,k) counting, not necessarily connected, k-regular simple graphs on n vertices with girth exactly 3. 8
 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 4, 5, 3, 1, 1, 0, 0, 2, 0, 16, 0, 4, 0, 1, 0, 0, 2, 15, 58, 59, 21, 5, 1, 1, 0, 0, 3, 0, 264, 0, 266, 0, 6, 0, 1, 0, 0, 4, 71, 1535, 7848, 7848, 1547, 94, 9, 1, 1, 0, 0, 5, 0, 10755, 0, 367860, 0, 10786, 0, 10, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,26 LINKS Jason Kimberley, Table of i, a(i)=E(n,k) for i = 1..136 (n = 1..16) Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth exactly g FORMULA E(n,k) = A186733(n,k) + A210703(n,k), noting that A210703 is a tabf. E(n,k) = A051031(n,k) - A185304(n,k), noting that A185304 is a tabf. EXAMPLE 01: 0; 02: 0, 0; 03: 0, 0, 1; 04: 0, 0, 0, 1; 05: 0, 0, 0, 0, 1; 06: 0, 0, 1, 1, 1, 1; 07: 0, 0, 1, 0, 2, 0, 1; 08: 0, 0, 1, 4, 5, 3, 1, 1; 09: 0, 0, 2, 0, 16, 0, 4, 0, 1; 10: 0, 0, 2, 15, 58, 59, 21, 5, 1, 1; 11: 0, 0, 3, 0, 264, 0, 266, 0, 6, 0, 1; 12: 0, 0, 4, 71, 1535, 7848, 7848, 1547, 94, 9, 1, 1; 13: 0, 0, 5, 0, 10755, 0, 367860, 0, 10786, 0, 10, 0, 1; 14: 0, 0, 6, 428, 87973, 3459379, 21609300, 21609300, 3459386, 88193, 540, 13, 1, 1; 15: 0, 0, 9, 0, 803973, 0, 1470293675, 0, 1470293676, 0, 805579, 0, 17, 0, 1; 16: 0, 0, 10, 3406, 8020967, 2585136353, 113314233804, 733351105934, 733351105934, 113314233813, 2585136741, 8037796, 4207, 21, 1, 1; CROSSREFS The sum of the n-th row of this sequence is A198313(n). Not necessarily connected k-regular simple graphs girth exactly 3: A198313 (any k), this sequence (triangle); fixed k: A026796 (k=2), A185133 (k=3), A185143 (k=4), A185153 (k=5), A185163 (k=6). Sequence in context: A366784 A217540 A226861 * A363051 A278515 A285709 Adjacent sequences: A185640 A185641 A185642 * A185644 A185645 A185646 KEYWORD nonn,hard,tabl AUTHOR Jason Kimberley, Feb 07 2013 STATUS approved

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Last modified December 11 08:46 EST 2023. Contains 367722 sequences. (Running on oeis4.)