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Search: id:A111636
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| A111636 |
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Triangle read by rows: T(n,k) (0<=k<=n) is the number of labeled graphs having k blue nodes and n-k green ones, and only nodes of different colors can be joined by an edge. |
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4
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| 1, 1, 1, 4, 1, 1, 12, 12, 1, 1, 32, 96, 32, 1, 1, 80, 640, 640, 80, 1, 1, 192, 3840, 10240, 3840, 192, 1, 1, 448, 21504, 143360, 143360, 21504, 448, 1, 1, 1024, 114688, 1835008, 4587520, 1835008, 114688, 1024, 1, 1, 2304, 589824, 22020096, 132120576
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Row sums yield A047863. T(2n,n)=A111637(n). T(n,1)=A001787(n).
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REFERENCES
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H. S. Wilf, Generatingfunctionology, 2nd edn., Academic Press, NY, 1994, p. 88, Eq. 3.11.2.
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FORMULA
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T(n, k)=2^[k(n-k)]*C(n, k).
Matrix log yields triangle A134530, where A134530(n,k) = A134531(n-k)*(2^k)^(n-k)*C(n,k). - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 11 2007
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EXAMPLE
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T(2,1)=4 because we have B G, B--G, G B, and G--B, where B (G) stands for a blue (green) node and -- denotes an edge.
Triangle starts:
1;
1,1;
1,4,1;
1,12,12,1;
1,32,96,32,1;
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MAPLE
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T:=(n, k)->binomial(n, k)*2^(k*(n-k)): for n from 0 to 9 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A047863, A111637, A001787.
Cf. A134530 (matrix log), A134531.
Sequence in context: A080416 A099759 A072590 this_sequence A051433 A140070 A101275
Adjacent sequences: A111633 A111634 A111635 this_sequence A111637 A111638 A111639
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 09 2005
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