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
Examples
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 ... ...
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
Programs
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Mathematica
T[m_, n_] := m^n + n^m - Min[m, n]! StirlingS2[Max[m, n], Min[m, n]] (* Eric W. Weisstein, Aug 10 2017 *)
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PARI
T(m,n) = m^n + n^m - if(n<=m, n!*stirling(m,n,2), m!*stirling(n,m,2));
Formula
T(m, n) = T(n, m).
T(n, k) = k^n + n^k - k! * stirling2(n,k) for k<=n.