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A204269
Symmetric matrix: f(i,j)=floor[(i+j+2)/4]-floor[(i+j)/4], by (constant) antidiagonals.
8
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, 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, 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
OFFSET
1
COMMENTS
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:
Matrix................Permanent of n-th submatrix
A204269=D204549.......A204422
A204545=D204269.......A204546
A204547=D204545.......A204548
A204549=D204547.......A204550
EXAMPLE
Northwest corner:
1 1 0 0 1 1 0 0
1 0 0 1 1 0 0 1
0 0 1 1 0 0 1 1
0 1 1 0 0 1 1 0
1 1 0 0 1 1 0 0
1 0 0 1 1 0 0 1
0 0 1 1 0 0 1 1
0 1 1 0 0 1 1 0
MATHEMATICA
f[i_, j_] := Floor[(i + j + 2)/4] - Floor[(i + j)/4];
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
{n, 1, 14}, {i, 1, n}]] (* A204269 *)
Permanent[m_] :=
With[{a = Array[x, Length[m]]},
Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 22}] (* A204422 *)
CROSSREFS
Sequence in context: A014087 A014042 A014075 * A371690 A179830 A266216
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 16 2012
STATUS
approved