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A174585 Let J_n be n X n matrix which contains 1's only, I=I_n be the n X n identity matrix and P=P_n be the incidence matrix of the cycle (1,2,3,...,n). Then a(n) is the number of (0,1,2) n X n matrices A<=2(J_n-I-P-P^2-P^3) with exactly one 1 and one 2 in every row and column.

%I A174585 #5 Jul 22 2025 07:54:21
%S A174585 0,2,132,9800,1309928
%N A174585 Let J_n be n X n matrix which contains 1's only, I=I_n be the n X n identity matrix and P=P_n be the incidence matrix of the cycle (1,2,3,...,n). Then a(n) is the number of (0,1,2) n X n matrices A<=2(J_n-I-P-P^2-P^3) with exactly one 1 and one 2 in every row and column.
%D A174585 V. S. Shevelev, Development of the rook technique for calculating the cyclic indicators of (0,1)-matrices, Izvestia Vuzov of the North-Caucasus region, Nature sciences 4 (1996), 21-28 (in Russian).
%D A174585 S. E. Grigorchuk, V. S. Shevelev, An algorithm of computing the cyclic indicator of couples discordant permutations with restricted position, Izvestia Vuzov of the North-Caucasus region, Nature sciences 3 (1997), 5-13 (in Russian).
%Y A174585 A001499 A007107 A082491 A000186 A174564 A174580 A174581 A174582 A174584
%K A174585 nonn,uned
%O A174585 5,2
%A A174585 _Vladimir Shevelev_, Mar 23 2010