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A014377
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Number of connected regular graphs of degree 7 with 2n nodes.
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20
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1, 0, 0, 0, 1, 5, 1547, 21609301, 733351105934, 42700033549946250, 4073194598236125132578, 613969628444792223002008202, 141515621596238755266884806115631
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listen;
history;
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OFFSET
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0,6
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REFERENCES
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CRC Handbook of Combinatorial Designs, 1996, p. 648.
I. A. Faradzev, Constructive enumeration of combinatorial objects, pp. 131-135 of Problèmes combinatoires et théorie des graphes (Orsay, 9-13 Juillet 1976). Colloq. Internat. du C.N.R.S., No. 260, Centre Nat. Recherche Scient., Paris, 1978.
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LINKS
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FORMULA
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This sequence is the inverse Euler transformation of A165628.
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EXAMPLE
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a(0)=1 because the null graph (with no vertices) is vacuously 7-regular and connected.
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CROSSREFS
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7-regular simple graphs: this sequence (connected), A165877 (disconnected), A165628 (not necessarily connected).
Connected regular simple graphs A005177 (any degree), A068934 (triangular array), specified degree k: A002851 (k=3), A006820 (k=4), A006821 (k=5), A006822 (k=6), this sequence (k=7), A014378 (k=8), A014381 (k=9), A014382 (k=10), A014384 (k=11).
Connected 7-regular simple graphs with girth at least g: this sequence (g=3), A181153 (g=4).
Connected 7-regular simple graphs with girth exactly g: A184963 (g=3), A184964 (g=4), A184965 (g=5). (End)
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KEYWORD
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nonn,nice,hard,more
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AUTHOR
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EXTENSIONS
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Term a(8) (on Meringer's page) was found from running Meringer's GENREG for 325 processor days at U. Newcastle by Jason Kimberley, Oct 02 2009
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STATUS
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approved
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