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A360918 Array read by antidiagonals: T(m,n) is the number of maximum induced trees in the grid graph P_m X P_n.

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%I A360918 #11 Feb 16 2025 08:34:04
%S A360918 1,1,1,1,4,1,1,2,2,1,1,10,10,10,1,1,4,26,26,4,1,1,24,2,32,2,24,1,1,8,
%T A360918 10,50,50,10,8,1,1,56,50,56,22,56,50,56,1,1,16,194,64,608,608,64,194,
%U A360918 16,1,1,128,4,72,182,4120,182,72,4,128,1,1,32,32,80,16,208,208,16,80,32,32,1
%N A360918 Array read by antidiagonals: T(m,n) is the number of maximum induced trees in the grid graph P_m X P_n.
%C A360918 A maximum induced tree is an induced tree of greatest size.
%H A360918 Andrew Howroyd, <a href="/A360918/b360918.txt">Table of n, a(n) for n = 1..435</a>
%H A360918 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>.
%F A360918 T(m,n) = T(n,m).
%e A360918 Array begins:
%e A360918 ===============================================
%e A360918 m\n| 1  2   3  4   5     6    7     8     9 ...
%e A360918 ---+-------------------------------------------
%e A360918 1  | 1  1   1  1   1     1    1     1     1 ...
%e A360918 2  | 1  4   2 10   4    24    8    56    16 ...
%e A360918 3  | 1  2  10 26   2    10   50   194     4 ...
%e A360918 4  | 1 10  26 32  50    56   64    72    80 ...
%e A360918 5  | 1  4   2 50  22   608  182    16     2 ...
%e A360918 6  | 1 24  10 56 608  4120  208  1968 22716 ...
%e A360918 7  | 1  8  50 64 182   208  488   560  1050 ...
%e A360918 8  | 1 56 194 72  16  1968  560 65864 14340 ...
%e A360918 9  | 1 16   4 80   2 22716 1050 14340   166 ...
%e A360918    ...
%Y A360918 Main diagonal is A360919.
%Y A360918 Cf. A360202, A360847, A360913, A360916, A360920 (maximum sizes).
%K A360918 nonn,tabl
%O A360918 1,5
%A A360918 _Andrew Howroyd_, Feb 26 2023