A204551 Symmetric matrix: f(i,j)=floor[(2i+2j+1)/4]-floor[(i+j)/4], by (constant) antidiagonals.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset

1,11

Comments

For n>=1, the number of occurrences of n is 16n-6. 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

A204551..............A204552

A204553=D204551......A204554

A204560=D204553......A204561

A204562=D204560......A204563

Links

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

Example

Northwest corner:
1 1 1 1 2 2 2 2 3
1 1 1 2 2 2 2 3 3
1 1 2 2 2 2 3 3 3
1 2 2 2 2 3 3 3 3
2 2 2 2 3 3 3 3 4
2 2 2 3 3 3 3 4 4
2 3 3 3 3 4 4 4 4

Mathematica

f[i_, j_] :=
Floor[(2 i + 2 j + 1)/4] - Floor[(i + j)/4];
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[16]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
  {n, 1, 14}, {i, 1, n}]]    (* A204551 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 15}]  (* A204552 *)

Crossrefs

Cf. A204551, A204296.

Sequence in context: A121902 A087103 A287091 * A292563 A362367 A211661

Adjacent sequences: A204548 A204549 A204550 * A204552 A204553 A204554

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 16 2012

Status

approved