login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Number of 3 X 3 arrays of squares of integers, symmetric about both diagonal and antidiagonal, with all rows summing to n.
0

%I #9 May 20 2021 15:48:23

%S 1,2,2,1,2,0,2,0,2,4,0,2,1,0,0,0,2,2,4,2,0,0,2,0,2,4,0,3,0,0,0,0,2,4,

%T 4,0,4,0,2,0,0,4,0,2,2,0,0,0,1,2,4,5,0,0,4,0,0,4,0,2,0,0,0,0,2,0,6,2,

%U 2,0,0,0,4,2,0,3,2,0,0,0,0,8,2,2,0,0,2,0,2,4,0,0,0,0,0,0,2,2,2,7,4,0,4,0,0,0,0,2

%N Number of 3 X 3 arrays of squares of integers, symmetric about both diagonal and antidiagonal, with all rows summing to n.

%C a(n) is nonzero if and only if n = x^2 + 2*y^2 for some integers x and y if and only if n is in A002479. - _Michael Somos_, Dec 15 2011

%e All solutions for n=9

%e ...0.0.9...1.4.4...4.4.1...9.0.0

%e ...0.9.0...4.1.4...4.1.4...0.9.0

%e ...9.0.0...4.4.1...1.4.4...0.0.9

%Y Cf. A002479.

%K nonn

%O 0,2

%A _R. H. Hardin_ Feb 09 2009