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A286912 Array read by antidiagonals: T(m,n) = number of edge covers in the grid graph P_m X P_n.

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%I A286912 #17 Feb 16 2025 08:33:45
%S A286912 0,1,1,1,7,1,2,43,43,2,3,277,969,277,3,5,1777,23663,23663,1777,5,8,
%T A286912 11407,571099,2180738,571099,11407,8,13,73219,13807469,198906617,
%U A286912 198906617,13807469,73219,13,21,469981,333735575,18169793971,68534828391,18169793971,333735575,469981,21
%N A286912 Array read by antidiagonals: T(m,n) = number of edge covers in the grid graph P_m X P_n.
%H A286912 Andrew Howroyd, <a href="/A286912/b286912.txt">Table of n, a(n) for n = 1..276</a>
%H A286912 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCover.html">Edge Cover</a>
%H A286912 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%e A286912 Table starts:
%e A286912 ======================================================================
%e A286912 m\n| 1     2        3           4              5                 6
%e A286912 ---|------------------------------------------------------------------
%e A286912 1  | 0     1        1           2              3                 5 ...
%e A286912 2  | 1     7       43         277           1777             11407 ...
%e A286912 3  | 1    43      969       23663         571099          13807469 ...
%e A286912 4  | 2   277    23663     2180738      198906617       18169793971 ...
%e A286912 5  | 3  1777   571099   198906617    68534828391    23650967140325 ...
%e A286912 6  | 5 11407 13807469 18169793971 23650967140325 30833670159649637 ...
%e A286912 ...
%Y A286912 Rows 1-3 are A000045(n-1), A286911, A288031.
%Y A286912 Main diagonal is A286913.
%Y A286912 Cf. A210662, A099390, A089934, A218354.
%K A286912 nonn,tabl
%O A286912 1,5
%A A286912 _Andrew Howroyd_, May 15 2017
%E A286912 T(1,1) corrected by _Andrew Howroyd_, Jun 04 2017