|
|
A277219
|
|
Triangle read by rows: T(n,k) is the number of independent sets of size k over all simple labeled graphs on n nodes, n>=0, 0<=k<=n.
|
|
1
|
|
|
1, 1, 1, 2, 4, 1, 8, 24, 12, 1, 64, 256, 192, 32, 1, 1024, 5120, 5120, 1280, 80, 1, 32768, 196608, 245760, 81920, 7680, 192, 1, 2097152, 14680064, 22020096, 9175040, 1146880, 43008, 448, 1, 268435456, 2147483648, 3758096384, 1879048192, 293601280, 14680064, 229376, 1024, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
Equivalently, T(n,k) is the number of size k cliques over all simple labeled graphs on n vertices.
|
|
LINKS
|
|
|
FORMULA
|
T(n,k) = 2^binomial(n,2)*binomial(n,k)/2^binomial(k,2).
|
|
EXAMPLE
|
Triangle begins:
1;
1, 1;
2, 4, 1;
8, 24, 12, 1;
64, 256, 192, 32, 1;
1024, 5120, 5120, 1280, 80, 1;
32768, 196608, 245760, 81920, 7680, 192, 1;
...
|
|
MAPLE
|
seq(seq(2^(n*(n-1)/2-k*(k-1)/2)*binomial(n, k), k=0..n), n=0..10); # Robert Israel, Oct 06 2016
|
|
MATHEMATICA
|
Table[Table[2^Binomial[n, 2] Binomial[n, k]/2^Binomial[k, 2], {k, 0, n}], {n, 0, 7}] // Grid
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|