A352550 a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 5.

1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2

Offset: 1

Author

N. J. A. Sloane, Mar 20 2022

Keywords

• nonn

Links

• Don Zagier, On the Number of n-Element Modules Over the Ring of Integers in a Quadratic Number Field [Based on email to N. J. A. Sloane, March 18 2022]

Crossrefs

Cf. A038540, A038541, A248107, A352551-A352567.

Programs

PARI

\\ Don Zagier, Mar 18 2022
PZ(D,m=20) = Z=dirmul(vector(m,n,1),vD=vector(m,n,kronecker(D,n))); v=Z; \
for(j=2,log(m)/log(2), V=v*0;for(k=1,m^(1/j),V[k^j]=Z[k]);v=dirmul(v,V)); v
PZ(5,100)