cp's OEIS Frontend

A174582 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) with exactly one 1 and one 2 in every row and column.

%I A174582 #5 Jul 22 2025 07:54:07
%S A174582 0,2,72,3722,329192,32842446
%N A174582 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) with exactly one 1 and one 2 in every row and column.
%D A174582 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 A174582 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 A174582 A001499 A007107 A082491 A000186 A174564 A174580 A174581
%K A174582 nonn,uned
%O A174582 4,2
%A A174582 _Vladimir Shevelev_, Mar 23 2010