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Symmetric matrix: f(i,j)=floor[(i+j+2)/4]-floor[(i+j)/4], by (constant) antidiagonals.
8

%I #9 Jan 27 2018 06:35:07

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

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

%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)/4], by (constant) antidiagonals.

%C A block matrix over {0,1}. In the following guide to related matrices and permanents, Duvwxyz represents the matrix remaining after row 1 of the matrix Auvwxyz is deleted:

%C Matrix................Permanent of n-th submatrix

%C A204269=D204549.......A204422

%C A204545=D204269.......A204546

%C A204547=D204545.......A204548

%C A204549=D204547.......A204550

%H G. C. Greubel, <a href="/A204269/b204269.txt">Table of n, a(n) for the first 100 antidiagonals</a>

%e Northwest corner:

%e 1 1 0 0 1 1 0 0

%e 1 0 0 1 1 0 0 1

%e 0 0 1 1 0 0 1 1

%e 0 1 1 0 0 1 1 0

%e 1 1 0 0 1 1 0 0

%e 1 0 0 1 1 0 0 1

%e 0 0 1 1 0 0 1 1

%e 0 1 1 0 0 1 1 0

%t f[i_, j_] := Floor[(i + j + 2)/4] - Floor[(i + j)/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}]] (* A204269 *)

%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}] (* A204422 *)

%Y Cf. A204448, A204435.

%K nonn,tabl

%O 1

%A _Clark Kimberling_, Jan 16 2012