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Search: id:A000685
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| A000685 |
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Number of 3-colored labeled graphs on n nodes.
(Formerly M3995 N1656)
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+0
2
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| 1, 5, 41, 545, 11681, 402305, 22207361, 1961396225, 276825510401, 62368881977345, 22413909724518401, 12840603873823473665, 11720394922432296755201, 17037597932370037286600705
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Sequence represents 1/3 of the number of 3-colored labeled graphs on n nodes. Indeed, on p. 413 of the Read paper, column 3 is 3,15,123,1635,..; or see A047863. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 06 2004
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REFERENCES
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R. C. Read, The number of k-colored graphs on labeled nodes, Canad. J. Math., 12 (1960), 410-414.
R. C. Read, personal communication.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..50
S. R. Finch, Bipartite, k-colorable and k-colored graphs (3*A000685)
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FORMULA
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a(n)=(1/3)sum(binomial(n, j)*2^[j(n-j)]*c(j), j=0..n), where c(n)=sum(binomial(n, i)*2^[i(n-i)], i=0..n)=A047863(n) - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 06 2004
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MAPLE
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c[0]:=1: for n from 1 to 30 do c[n]:=sum(binomial(n, i)*2^(i*(n-i)), i=0..n) od: a:=n->(1/3)*sum(binomial(n, j)*2^(j*(n-j))*c[j], j=0..n): seq(a(n), n=1..19);
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CROSSREFS
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Cf. A000683, A047863.
Adjacent sequences: A000682 A000683 A000684 this_sequence A000686 A000687 A000688
Sequence in context: A143415 A056545 A009755 this_sequence A139034 A073854 A104344
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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EXTENSIONS
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More terms from Pab Ter (pabrlos(AT)yahoo.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), May 05 2004
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