A204441 - OEIS

%I #6 Mar 30 2012 18:58:08

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

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

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

%N Symmetric matrix: f(i,j)=floor[(i+j+2)/4]-floor[(i+j-1)/4], 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 1 1 1 0 1 1 1 0

%e 1 1 0 1 1 1 0 1

%e 1 0 1 1 1 0 1 1

%e 0 1 1 1 0 1 1 1

%e 1 1 1 0 1 1 1 0

%e 1 1 0 1 1 1 0 1

%e 1 0 1 1 1 0 1 1

%e 0 1 1 1 0 1 1 1

%t f[i_, j_] :=

%t  Floor[(i + j + 2)/4] - Floor[(i + j - 1)/4];

%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}]]        (* A204441 *)

%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}]    (* A204442 *)

%Y Cf. A204442, A204435.

%K nonn,tabl

%O 1

%A _Clark Kimberling_, Jan 15 2012