|
Search: id:A046858
|
|
|
| A046858 |
|
Irregular triangle read by rows: T(n,k) = number of directed graphs-with-loops with n nodes and k arcs (n >= 0, 0 <= k <= n(n+1)). |
|
+0
2
|
|
| 1, 1, 1, 1, 2, 4, 2, 1, 1, 2, 8, 17, 24, 24, 17, 8, 2, 1, 1, 2, 9, 32, 95, 203, 373, 515, 584, 515, 373, 203, 95, 32, 9, 2, 1, 1, 2, 9, 36, 157, 549, 1692, 4374, 9626, 17874, 28373, 38486, 44805, 44805, 38486, 28373, 17874, 9626, 4374, 1692, 549, 157, 36, 9, 2, 1, 1
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Equivalently, T(n,k) = number of relations on n-set with strength k (n >= 0, 0<=k<=n^2).
|
|
REFERENCES
|
W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. Ann., 174 (1967), 53-78.
|
|
LINKS
|
W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. Ann., 174 (1967), 53-78.
|
|
EXAMPLE
|
Triangle begins:
[1],
[1, 1],
[1, 2, 4, 2, 1],
[1, 2, 8, 17, 24, 24, 17, 8, 2, 1],
[1, 2, 9, 32, 95, 203, 373, 515, 584, 515, 373, 203, 95, 32, 9, 2, 1] (the last batch giving the numbers of directed graphs with loops on 4 nodes and from 0 to 16 arcs).
|
|
CROSSREFS
|
Cf. A000595.
Sequence in context: A094239 A105023 A052285 this_sequence A132823 A059317 A087266
Adjacent sequences: A046855 A046856 A046857 this_sequence A046859 A046860 A046861
|
|
KEYWORD
|
nonn,tabf,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 07 2000
Edited by N. J. A. Sloane (njas(AT)research.att.com) Apr 16 2008 at the suggestion of Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 24 2008
|
|
|
Search completed in 0.002 seconds
|
