A156381 Number of 3 X 3 arrays of squares of integers, symmetric about both diagonal and antidiagonal, with all rows summing to n.

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, 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, 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

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..107.

Example

All solutions for n=9
...0.0.9...1.4.4...4.4.1...9.0.0
...0.9.0...4.1.4...4.1.4...0.9.0
...9.0.0...4.4.1...1.4.4...0.0.9

Crossrefs

Cf. A002479.

Sequence in context: A129402 A128580 A104405 * A089077 A203398 A339275

Adjacent sequences: A156378 A156379 A156380 * A156382 A156383 A156384

Keyword

nonn

Author

R. H. Hardin Feb 09 2009

Status

approved