A204260 Symmetric matrix given by f(i,j)=ceiling(i*j/(i+j)) .

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

Offset: 1

Author

Clark Kimberling, Jan 14 2012

Keywords

• nonn
• tabl

Examples

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

Crossrefs

Cf. A204261.

Programs

Mathematica

f[i_, j_] := Ceiling[i*j/(i + j)];
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, 12}, {i, 1, n}]]  (* A204260 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 14}]  (* A204261 *)