A204437 - OEIS

%I #5 Mar 30 2012 18:58:08

%S 0,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,

%U 1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1

%N Symmetric matrix: f(i,j)=((i+j+1)^2 mod 3), by (constant) antidiagonals.

%C A block matrix over {0,1}.  For guides to related matrices and permanents, see A204435 and A204263.

%e Northwest corner:

%e 0 1 1 0 1 1

%e 1 1 0 1 1 0

%e 1 0 1 1 0 1

%e 0 1 1 0 1 1

%e 1 1 0 1 1 0

%e 1 0 1 1 0 1

%t f[i_, j_] := Mod[(1 + i + j)^2, 3];

%t m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

%t TableForm[m[8]] (* 8x8 principal submatrix *)

%t Flatten[Table[f[i, n + 1 - i],

%t   {n, 1, 14}, {i, 1, n}]]         (* A204437 *)

%t Permanent[m_] :=

%t   With[{a = Array[x, Length[m]]},

%t    Coefficient[Times @@ (m.a), Times @@ a]];

%t Table[Permanent[m[n]], {n, 1, 22}]   (* A204438 *)

%Y Cf. A204438, A204435.

%K nonn,tabl

%O 1

%A _Clark Kimberling_, Jan 15 2012