A341847 Array read by antidiagonals: T(n,m) is the number of maximal matchings in the rook graph K_n X K_m.

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

Andrew Howroyd, Table of n, a(n) for n = 0..275

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: A106693 A107335 A341850 * A200223 A236228 A082391

Adjacent sequences: A341844 A341845 A341846 * A341848 A341849 A341850

Keyword

nonn,tabl

Author

Andrew Howroyd, Feb 21 2021

Status

approved