|
Search: id:A085463
|
|
|
| A085463 |
|
Number of 5-tuples (v1,v2,v3,v4,v5) of nonnegative integers less than n such that v1<=v4, v1<=v5, v2<=v4, v2<=v5 and v3<=v4. |
|
+0
1
|
|
| 1, 12, 63, 219, 594, 1365, 2786, 5202, 9063, 14938, 23529, 35685, 52416, 74907, 104532, 142868, 191709, 253080, 329251, 422751, 536382, 673233, 836694, 1030470, 1258595, 1525446, 1835757, 2194633, 2607564, 3080439, 3619560, 4231656
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Number of monotone n-weightings of a certain connected bipartite digraph. 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.
|
|
LINKS
|
Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.
|
|
FORMULA
|
a(n) = n+10*binomial(n, 2)+30*binomial(n, 3)+35*binomial(n, 4)+14*binomial(n, 5) = 1/120*n*(n+1)*(2*n+1)*(7*n^2+7*n+6).
|
|
CROSSREFS
|
Cf. A006322, A006325, A079547, A085461-A085465.
Sequence in context: A045822 A065595 A092224 this_sequence A051922 A027810 A012875
Adjacent sequences: A085460 A085461 A085462 this_sequence A085464 A085465 A085466
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Goran Kilibarda, Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 01 2003
|
|
|
Search completed in 0.002 seconds
|
