A263850 Let R = Z((1+sqrt{5})/2) denote the ring of integers in the real quadratic number field of discriminant 5. Then a(n) is the number of ways of writing a totally positive element of norm n as a sum of three squares in R, or 0 if there is no totally positive element of norm n.

1, 6, 0, 0, 12, 24, 0, 0, 0, 32, 0, 24, 0, 0, 0, 0, 54, 0, 0, 24, 24, 0, 0, 0, 0, 30, 0, 0, 0, 24, 0, 48, 0, 0, 0, 0, 48, 0, 0, 0, 0, 96, 0, 0, 24, 48, 0, 0, 0, 96, 0, 0, 0, 0, 0, 48, 0, 0, 0, 24, 0, 120, 0, 0, 108, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 72, 0, 0, 48, 120, 54, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0

Offset

0,2

Comments

The terms were computed with the aid of Magma by David Durstoff, Nov 11 2015. See A263849 for further information.

References

Maass, Hans. Über die Darstellung total positiver Zahlen des Körpers R (sqrt(5)) als Summe von drei Quadraten, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg. Vol. 14. No. 1, pp. 185-191, 1941.

Links

Table of n, a(n) for n=0..92.

Crossrefs

Cf. A263849 (another version of this sequence), A031363, A035187.

Sequence in context: A037215 A028592 A243254 * A341797 A340905 A210446

Adjacent sequences: A263847 A263848 A263849 * A263851 A263852 A263853

Keyword

nonn

Author

N. J. A. Sloane, Nov 18 2015

Status

approved