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 A185305 Triangular array E(n,k) counting not necessarily connected k-regular simple graphs on n vertices with girth at least 5. 5
 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 0, 2, 0, 1, 1, 3, 2, 1, 0, 3, 0, 1, 1, 4, 9, 1, 0, 5, 0, 1, 1, 6, 49, 1, 0, 7, 0, 1, 1, 9, 455, 1, 0, 10, 0, 1, 1, 1, 13, 5784, 2, 1, 0, 15, 0, 8, 1, 1, 18, 90940, 131, 1, 0, 21, 0, 3917, 1, 1, 26, 1620491, 123859 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,25 COMMENTS Row sums give A185315. LINKS Jason Kimberley, Table of n, a(i)=E(n,k) for i = 1..108 (n = 1..28) Jason Kimberley, Not necessarily connected k-regular graphs with girth at least 5 FORMULA E(n,k) = A186715(n,k) + A185205(n,k). EXAMPLE 01: 1; 02: 1, 1; 03: 1, 0; 04: 1, 1; 05: 1, 0, 1; 06: 1, 1, 1; 07: 1, 0, 1; 08: 1, 1, 1; 09: 1, 0, 1; 10: 1, 1, 2, 1; 11: 1, 0, 2, 0; 12: 1, 1, 3, 2; 13: 1, 0, 3, 0; 14: 1, 1, 4, 9; 15: 1, 0, 5, 0; 16: 1, 1, 6, 49; 17: 1, 0, 7, 0; 18: 1, 1, 9, 455; 19: 1, 0, 10, 0, 1; 20: 1, 1, 13, 5784, 2; 21: 1, 0, 15, 0, 8; 22: 1, 1, 18, 90940, 131; 23: 1, 0, 21, 0, 3917; 24: 1, 1, 26, 1620491, 123859; 25: 1, 0, 30, 0, 4131991; 26: 1, 1, 36, 31478649, 132160608; 27: 1, 0, 42, 0, 4018022149; 28: 1, 1, 50, 656784488, 118369811960; CROSSREFS Not necessarily connected k-regular simple graphs with girth at least 5: A185315 (any k), this sequence (triangle); specified degree k: A185325 (k=2), A185335 (k=3). Sequence in context: A253559 A136167 A140748 * A259875 A070821 A165890 Adjacent sequences:  A185302 A185303 A185304 * A185306 A185307 A185308 KEYWORD nonn,hard,tabf AUTHOR Jason Kimberley, Feb 21 2013 STATUS approved

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)