A204562 Symmetric matrix: f(i,j) = floor((2i+2j+6)/4)-floor((i+j+3)/4), by (constant) antidiagonals.

1, 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, 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, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5

Offset

1,2

Comments

For n>=2, the number of occurrences of n is 16n-18. For a guide to related sequences and permanents, see A204551.

Links

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

Example

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

Mathematica

f[i_, j_] :=
Floor[(2 i + 2 j + 6)/4] - Floor[(i + j + 3)/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}]]      (* A204562 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 17}]   (* A204563 *)

Crossrefs

Cf. A204563, A204551.

Sequence in context: A107609 A243113 A258198 * A135660 A163858 A236362

Adjacent sequences: A204559 A204560 A204561 * A204563 A204564 A204565

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 16 2012

Status

approved