A163123 a(n) = number of integral positive unordered pairs (x,y) such that x^2+n*y=z^2 and n*x+y^2=w^2.

0, 0, 2, 0, 4, 2, 7, 3, 10, 4, 8, 9, 15, 7, 19, 14, 11, 9, 9

Offset

1,3

Comments

Solutions (x,y) and (y,x) count only once.

Links

Table of n, a(n) for n=1..19.

Example

Example:
a(6)=2 since the system of two equations
1. x^2+6y=z^2
2. 6x+y^2=w^2
has the following 2 solutions:
s1. (x,y)=(2,2) yielding 2^2+6*2=16=4^2 and 6*2+2^2=16=4^2.
s2. (x,y)=(22,32) yielding 22^2+6*32=26^2 and 6*22+32^2=34^2.
There are no solutions for n= 1, 2, 4.

Crossrefs

Sequence in context: A216960 A285348 A361008 * A194346 A328598 A284010

Adjacent sequences: A163120 A163121 A163122 * A163124 A163125 A163126

Keyword

nonn

Author

Carmine Suriano, Jul 21 2009

Status

approved