login
A204545
Symmetric matrix: f(i,j)=floor[(i+j+3)/4]-floor[(i+j+1)/4], by (constant) antidiagonals.
3
1, 0, 0, 0, 0, 0, 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, 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, 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, 0, 0, 0, 0, 0, 0
OFFSET
1
COMMENTS
A block matrix over {0,1}. For a guide to related matrices and permanents, see A204269 and A204453.
EXAMPLE
Northwest corner:
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
1 1 0 0 1 1 0 0
MATHEMATICA
f[i_, j_] := Floor[(i + j + 3)/4] - Floor[(i + j + 1)/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}]] (* A204545 *)
Permanent[m_] :=
With[{a = Array[x, Length[m]]},
Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 22}] (* A204546 *)
CROSSREFS
Sequence in context: A333818 A111412 A080111 * A185116 A014034 A014059
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 16 2012
STATUS
approved