A103612 Number of solutions to 5+B^2=p^2+q^2 with B=2n, p,q>0 and 2p^2<5+B^2.

1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0

Offset

0,16

Comments

The number of matrices with entries in Z to G^2=G+1 not of the form gI or g'I (g, the golden number and g'=1-g are the solutions to x^2=x+1), hence of the form (1+p q-B | q+B 1-p) with p^2+q^2=5+B^2 is given by 8a(n) for n!=1 and by 4a(1)=4 for n=1.

Links

Table of n, a(n) for n=0..104.

Example

a(0)=1 because 5+0^2=5=1^2+2^2. a(15)=2 because 5+30^2=905=8^2+29^2=11^2+28^2.

Crossrefs

Cf. A104768.

Sequence in context: A245194 A351555 A215020 * A083913 A363855 A023670

Adjacent sequences: A103609 A103610 A103611 * A103613 A103614 A103615

Keyword

easy,nonn

Author

Michele Dondi (blazar(AT)lcm.mi.infn.it), Mar 24 2005

Status

approved