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A085465
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Number of monotone n-weightings of complete bipartite digraph K(3,3).
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6
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1, 15, 102, 442, 1443, 3885, 9100, 19188, 37269, 67771, 116754, 192270, 304759, 467481, 696984, 1013608, 1442025, 2011815, 2758078, 3722082, 4951947, 6503365, 8440356, 10836060, 13773565, 17346771, 21661290, 26835382, 33000927, 40304433
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A monotone n-(vertex) weighting of a digraph D=(V,E) is a function w: V -> {0,1,..,n-1} such that w(v1)<=w(v2) for every arc (v1,v2) from E.
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LINKS
| Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.
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FORMULA
| a(n) = n+13*binomial(n, 2)+60*binomial(n, 3)+120*binomial(n, 4)+108*binomial(n, 5)+36*binomial(n, 6) = 1/20*n*(n+1)*(n^2+1)*(n^2+2*n+2) = Sum_{i=1..n} ((n+1-i)^3-(n-i)^3)*i^3. More generally, number of monotone n-weightings of complete bipartite digraph K(s, t) is Sum_{i=1..n} ((n+1-i)^s-(n-i)^s)*i^t = Sum_{i=1..n} ((n+1-i)^t-(n-i)^t)*i^s.
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CROSSREFS
| Cf. A006322, A006325, A079547, A085461-A085465.
Sequence in context: A111370 A093739 A205431 * A205424 A102791 A160892
Adjacent sequences: A085462 A085463 A085464 * A085466 A085467 A085468
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KEYWORD
| nonn
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AUTHOR
| Goran Kilibarda, Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 01 2003
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