A082039 Symmetric square array defined by T(n,k) = k^2*n^2 + k*n + 1, read by antidiagonals.

1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 13, 21, 13, 1, 1, 21, 43, 43, 21, 1, 1, 31, 73, 91, 73, 31, 1, 1, 43, 111, 157, 157, 111, 43, 1, 1, 57, 157, 241, 273, 241, 157, 57, 1, 1, 73, 211, 343, 421, 421, 343, 211, 73, 1, 1, 91, 273, 463, 601, 651, 601, 463, 273, 91, 1, 1, 111, 343, 601, 813, 931, 931, 813, 601, 343, 111, 1

Offset

0,5

Links

Table of n, a(n) for n=0..77.

Formula

G.f.: (1-2*x-2*y+x^2+y^2+3*x^2*y^2-2*x^2*y-2*x*y^2+6*x*y)/((1-x)^3*(1-y)^3). - R. J. Mathar, Dec 11 2025

Example

Square array T(n,k) begins:
  1  1  1   1   1   1 ...
  1  3  7  13  21  31 ...
  1  7 21  43  73 111 ...
  1 13 43  91 157 241 ...
  1 21 73 157 273 421 ...
  ...

Crossrefs

Rows include A054569, A002061, A082040, A082041.

Main diagonal is A059826.

Cf. A082038.

Sequence in context: A146900 A132733 A347971 * A367505 A176331 A157836

Adjacent sequences: A082036 A082037 A082038 * A082040 A082041 A082042

Keyword

easy,nonn,tabl

Author

Paul Barry, Apr 02 2003

Status

approved