A290632 Array read by antidiagonals: T(m,n) = number of minimal dominating sets in the rook graph K_m X K_n.

1, 2, 2, 3, 6, 3, 4, 11, 11, 4, 5, 18, 48, 18, 5, 6, 27, 109, 109, 27, 6, 7, 38, 218, 488, 218, 38, 7, 8, 51, 405, 1409, 1409, 405, 51, 8, 9, 66, 724, 3832, 6130, 3832, 724, 66, 9, 10, 83, 1277, 10385, 21601, 21601, 10385, 1277, 83, 10

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275

Eric Weisstein's World of Mathematics, Minimal Dominating Set

Eric Weisstein's World of Mathematics, Rook Graph

Formula

T(m, n) = T(n, m).

T(n, k) = k^n + n^k - k! * stirling2(n,k) for k<=n.

Example

Array begins:
========================================================
m\n| 1  2    3     4      5       6       7        8
---|----------------------------------------------------
1  | 1  2    3     4      5       6       7        8 ...
2  | 2  6   11    18     27      38      51       66 ...
3  | 3 11   48   109    218     405     724     1277 ...
4  | 4 18  109   488   1409    3832   10385    28808 ...
5  | 5 27  218  1409   6130   21601   78132   297393 ...
6  | 6 38  405  3832  21601   92592  382465  1750240 ...
7  | 7 51  724 10385  78132  382465 1642046  7720833 ...
8  | 8 66 1277 28808 297393 1750240 7720833 33514112 ...
...

Mathematica

T[m_, n_] := m^n + n^m - Min[m, n]! StirlingS2[Max[m, n], Min[m, n]] (* Eric W. Weisstein, Aug 10 2017 *)

Prog

(PARI)
T(m, n) = m^n + n^m - if(n<=m, n!*stirling(m, n, 2), m!*stirling(n, m, 2));

Crossrefs

Main diagonal is A248744.

Cf. A287274.

Sequence in context: A190098 A272973 A272958 * A291543 A296320 A296396

Adjacent sequences: A290629 A290630 A290631 * A290633 A290634 A290635

Keyword

nonn,tabl

Author

Andrew Howroyd, Aug 07 2017

Status

approved