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

A174581

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