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A341847
Array read by antidiagonals: T(n,m) is the number of maximal matchings in the rook graph K_n X K_m.
6
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 3, 1, 1, 3, 10, 10, 3, 1, 1, 15, 40, 84, 40, 15, 1, 1, 15, 296, 852, 852, 296, 15, 1, 1, 105, 1576, 11580, 22368, 11580, 1576, 105, 1, 1, 105, 15352, 197640, 822528, 822528, 197640, 15352, 105, 1, 1, 945, 104000, 4314240, 38772864, 84961440, 38772864, 4314240, 104000, 945, 1
OFFSET
0,12
LINKS
Eric Weisstein's World of Mathematics, Maximal Independent Edge Set
Eric Weisstein's World of Mathematics, Rook Graph
FORMULA
T(n,m) = T(m,n).
EXAMPLE
Array begins:
=============================================================
n\m | 0 1 2 3 4 5 6
----+--------------------------------------------------------
0 | 1 1 1 1 1 1 1 ...
1 | 1 1 1 3 3 15 15 ...
2 | 1 1 2 10 40 296 1576 ...
3 | 1 3 10 84 852 11580 197640 ...
4 | 1 3 40 852 22368 822528 38772864 ...
5 | 1 15 296 11580 822528 84961440 12002446080 ...
6 | 1 15 1576 197640 38772864 12002446080 5429866337280 ...
...
CROSSREFS
Rows n=1..4 are A133221(n+1), A281433, A341848, A341849.
Main diagonal is A289198.
Cf. A270227 (matchings), A297471, A341850 (maximum matchings).
Sequence in context: A107335 A375782 A341850 * A200223 A236228 A082391
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Feb 21 2021
STATUS
approved