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A360913 Array read by antidiagonals: T(m,n) is the number of maximum induced cycles in the grid graph P_m X P_n.

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%I A360913 #10 Feb 16 2025 08:34:04
%S A360913 1,2,2,3,1,3,4,1,1,4,5,1,7,1,5,6,1,17,17,1,6,7,1,31,90,31,1,7,8,1,8,
%T A360913 284,284,8,1,8,9,1,40,9,1398,9,40,1,9,10,1,120,163,10,10,163,120,1,10,
%U A360913 11,1,8,1329,382,23,382,1329,8,1,11,12,1,64,128,6098,190,190,6098,128,64,1,12
%N A360913 Array read by antidiagonals: T(m,n) is the number of maximum induced cycles in the grid graph P_m X P_n.
%C A360913 A maximum induced cycle is an induced cycle of longest length.
%H A360913 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>.
%F A360913 T(m,n) = T(n,m).
%e A360913 Array begins:
%e A360913 =========================================
%e A360913 m\n| 2  3   4    5    6   7    8    9 ...
%e A360913 ---+-------------------------------------
%e A360913 2  | 1  2   3    4    5   6    7    8 ...
%e A360913 3  | 2  1   1    1    1   1    1    1 ...
%e A360913 4  | 3  1   7   17   31   8   40  120 ...
%e A360913 5  | 4  1  17   90  284   9  163 1329 ...
%e A360913 6  | 5  1  31  284 1398  10  382 6098 ...
%e A360913 7  | 6  1   8    9   10  23  190  388 ...
%e A360913 8  | 7  1  40  163  382 190 2100   80 ...
%e A360913 9  | 8  1 120 1329 6098 388   80 6840 ...
%e A360913   ...
%Y A360913 Main diagonal is A360914.
%Y A360913 Cf. A360196 (induced cycles), A360915 (lengths), A360916, A360918.
%K A360913 nonn,tabl
%O A360913 2,2
%A A360913 _Andrew Howroyd_, Feb 26 2023