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A006924
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Number of connected trivalent graphs with 2n nodes and girth exactly 4.
(Formerly M1526)
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15
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0, 0, 0, 1, 2, 5, 20, 101, 743, 7350, 91763, 1344782, 22160335, 401278984, 7885687604, 166870266608, 3781101495300
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| CRC Handbook of Combinatorial Designs, 1996, p. 647.
Gordon Royle, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| F. C. Bussemaker, S. Cobeljic, L. M. Cvetkovic and J. J. Seidel, Computer investigations of cubic graphs, T.H.-Report 76-WSK-01, Technological University Eindhoven, Dept. Mathematics, 1976.
Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth exactly g
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FORMULA
| a(n) = A014371(n) - A014372(n).
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CROSSREFS
| Connected k-regular simple graphs with girth exactly 4: this sequence (k=3), A184944 (k=4), A184954 (k=5), A184964 (k=6), A184974 (k=7), A184984 (k=8), A184994 (k=9).
Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); specified g: A006923 (g=3), this sequence (g=4), A006925 (g=5), A006926 (g=6), A006927 (g=7).
Connected 3-regular simple graphs with girth at least g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).
Sequence in context: A020001 A039909 A009551 * A152562 A006867 A170946
Adjacent sequences: A006921 A006922 A006923 * A006925 A006926 A006927
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KEYWORD
| nonn,hard,more,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Definition corrected to include "connected", and "girth at least 4" minus "girth at least 5" formula provided by Jason Kimberley, Dec 12 2009
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