A204545 Symmetric matrix: f(i,j)=floor[(i+j+3)/4]-floor[(i+j+1)/4], by (constant) antidiagonals.

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.

Links

Table of n, a(n) for n=1..99.

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

Cf. A204546, A204296.

Sequence in context: A333818 A111412 A080111 * A185116 A014034 A014059

Adjacent sequences: A204542 A204543 A204544 * A204546 A204547 A204548

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 16 2012

Status

approved