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

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%I A352550 #28 Nov 24 2023 21:17:00
%S A352550 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,
%T A352550 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,
%U A352550 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
%N A352550 a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 5.
%H A352550 Don Zagier, <a href="/A352550/a352550.txt">On the Number of n-Element Modules Over the Ring of Integers in a Quadratic Number Field</a> [Based on email to N. J. A. Sloane, March 18 2022]
%o A352550 (PARI) \\ Don Zagier, Mar 18 2022
%o A352550 PZ(D,m=20) = Z=dirmul(vector(m,n,1),vD=vector(m,n,kronecker(D,n))); v=Z; \
%o A352550 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
%o A352550 PZ(5,100)
%Y A352550 Cf. A038540, A038541, A248107, A352551-A352567.
%K A352550 nonn
%O A352550 1,11
%A A352550 _N. J. A. Sloane_, Mar 20 2022