A082039 - OEIS

%I #9 Dec 11 2025 12:05:58

%S 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,

%T 1,43,111,157,157,111,43,1,1,57,157,241,273,241,157,57,1,1,73,211,343,

%U 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

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

%F 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

%e Square array T(n,k) begins:

%e   1  1  1   1   1   1 ...

%e   1  3  7  13  21  31 ...

%e   1  7 21  43  73 111 ...

%e   1 13 43  91 157 241 ...

%e   1 21 73 157 273 421 ...

%e   ...

%Y Rows include A054569, A002061, A082040, A082041.

%Y Main diagonal is A059826.

%Y Cf. A082038.

%K easy,nonn,tabl

%O 0,5

%A _Paul Barry_, Apr 02 2003