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A006923
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Number of connected trivalent graphs with 2n nodes and with girth exactly 3.
(Formerly M2944)
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15
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1, 1, 3, 13, 63, 399, 3268, 33496, 412943, 5883727, 94159721, 1661723296, 31954666517, 663988090257, 14814445040728
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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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) = A002851(n) - A014371(n).
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CROSSREFS
| Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); specified g: this sequence (g=3), A006924 (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: A107097 A202837 A180111 * A011272 A200719 A065065
Adjacent sequences: A006920 A006921 A006922 * A006924 A006925 A006926
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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 3" minus "girth at least 4" formula provided by Jason Kimberley, Dec 12 2009
Terms a(14), a(15), and a(16) appended using "new" terms of A014371 by Jason Kimberley, Nov 16 2011
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