A204250 Symmetric matrix read by antidiagonals given by T(i,j)=i*j+i+j-2.

1, 3, 3, 5, 6, 5, 7, 9, 9, 7, 9, 12, 13, 12, 9, 11, 15, 17, 17, 15, 11, 13, 18, 21, 22, 21, 18, 13, 15, 21, 25, 27, 27, 25, 21, 15, 17, 24, 29, 32, 33, 32, 29, 24, 17, 19, 27, 33, 37, 39, 39, 37, 33, 27, 19, 21, 30, 37, 42, 45, 46, 45, 42, 37, 30, 21, 23, 33, 41, 47

Offset: 1

Author

Clark Kimberling, Jan 14 2012

Keywords

• nonn
• tabl

Examples

			Northwest corner:
1...3...5....7....9
3...6...9....12...15
5...9...13...17...21
7...12..17...22...27
		

Links

• David Singmaster, David Fielker, N. J. A. Sloane, Correspondence, August 1979

Crossrefs

Cf. A204251.

Programs

Mathematica

f[i_, j_] := i*j + i + j - 2;
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[5]] (* 5x5 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
  {n, 1, 12}, {i, 1, n}]]          (* A204250 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 14}] (* A204251 *)