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A288025 Array read by antidiagonals: T(m,n) = number of minimal edge covers in the grid graph P_m X P_n.

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%I A288025 #11 Feb 16 2025 08:33:47
%S A288025 0,1,1,1,2,1,1,6,6,1,2,17,38,17,2,2,45,190,190,45,2,3,120,1021,1834,
%T A288025 1021,120,3,4,324,5494,19988,19988,5494,324,4,5,873,29042,208186,
%U A288025 419710,208186,29042,873,5,7,2349,154772,2177591,8704085,8704085,2177591,154772,2349,7
%N A288025 Array read by antidiagonals: T(m,n) = number of minimal edge covers in the grid graph P_m X P_n.
%C A288025 A minimal edge cover is an edge cover such that the removal of any edge in the cover destroys the covering property. Equivalently, these are the edge covers whose connected components are stars. A minimal edge cover is not the same as a minimum edge cover.
%H A288025 Andrew Howroyd, <a href="/A288025/b288025.txt">Table of n, a(n) for n = 1..153</a>
%H A288025 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%H A288025 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalEdgeCover.html">Minimal Edge Cover</a>
%e A288025 Table starts:
%e A288025 ================================================================
%e A288025 m\n| 1   2     3       4         5           6             7
%e A288025 ---|------------------------------------------------------------
%e A288025 1  | 0   1     1       1         2           2             3 ...
%e A288025 2  | 1   2     6      17        45         120           324 ...
%e A288025 3  | 1   6    38     190      1021        5494         29042 ...
%e A288025 4  | 1  17   190    1834     19988      208186       2177591 ...
%e A288025 5  | 2  45  1021   19988    419710     8704085     179649371 ...
%e A288025 6  | 2 120  5494  208186   8704085   356269056   14484264119 ...
%e A288025 7  | 3 324 29042 2177591 179649371 14484264119 1163645044100 ...
%e A288025 ...
%Y A288025 Main diagonal is A288027.
%Y A288025 Rows 1-3 are A182097, A288029, A288030.
%Y A288025 Cf. A286912.
%K A288025 nonn,tabl
%O A288025 1,5
%A A288025 _Andrew Howroyd_, Jun 04 2017