A204447 Symmetric matrix: f(i,j)=floor[(i+j+5)/4]-floor[(i+j+2)/4], by (constant) antidiagonals.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 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, 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

Offset

1

Comments

A block matrix over {0,1}. For guides to related matrices and permanents, see A204435 and A204263.

Links

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

Example

Northwest corner:
0 1 1 1 0 1 1 1
1 1 1 0 1 1 1 0
1 1 0 1 1 1 0 1
1 0 1 1 1 0 1 1
0 1 1 1 0 1 1 1
1 1 1 0 1 1 1 0
1 1 0 1 1 1 0 1
1 0 1 1 1 0 1 1

Mathematica

f[i_, j_] :=
Floor[(i + j + 5)/4] - Floor[(i + j + 2)/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}]]     (* A204447 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 22}]    (* A204448 *)

Crossrefs

Cf. A204448, A204435.

Sequence in context: A164980 A252372 A168182 * A368905 A188642 A168046

Adjacent sequences: A204444 A204445 A204446 * A204448 A204449 A204450

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 15 2012

Status

approved