A204553 Symmetric matrix: f(i,j)=floor[(2i+2j+2)/4]-floor[(i+j+1)/4], by (constant) antidiagonals.

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, 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, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset

1,7

Comments

For n>=1, the number of occurrences of n is 16n-10. For a guide to related sequences and permanents, see A204551.

Links

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

Example

Northwest corner:
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
3 3 3 3 4 4 4 4 5

Mathematica

f[i_, j_] :=
Floor[(2 i + 2 j + 2)/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}]]     (* A204553 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 15}]  (* A204554 *)

Crossrefs

Cf. A204554, A204551.

Sequence in context: A343743 A069926 A077429 * A214455 A060417 A097944

Adjacent sequences: A204550 A204551 A204552 * A204554 A204555 A204556

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 16 2012

Status

approved