A328999 - OEIS

%I #17 Dec 18 2024 21:01:20

%S 1,4,2,4,2,4,4,0,4,4,0,0,0,4,8,4,4,0,0,4,4,0,0,4,2,0,4,8,4,4,2,4,0,4,

%T 4,4,4,0,4,0,16,0,0,0,0,4,0,0,4,0,4,4,2,8,0,4,4,0,0,4,0,4,0,4,4,0,16,

%U 0,0,4,2,4,0,4,0,0,0,8,4,16,2,0,0,4,4,4

%N Dirichlet g.f. = (Product_{primes p == 1 (mod 12)} (1+p^(-s))^2/(1-p^(-s))^2) * Product_{primes p == +-5 (mod 12)} (1+p^(-2*s))/(1-p^(-2*s)).

%H Michael Baake and Peter A. B. Pleasants, <a href="https://doi.org/10.1515/zna-1995-0802">Algebraic solution of the coincidence problem in two and three dimensions</a>, Zeitschrift für Naturforschung A 50.8 (1995): 711-717. See page 714.

%e The D.g.f. is 1 + 4/13^s + 2/25^s + 4/37^s + ... .

%o (PARI) a(n) = direuler(p = 2, 12*n-11, (1 + (p%12==1)*X)^2/(1 - (p%12==1)*X)^2 * (1 + ((p%12==5)+(p%12==7))*X^2)/(1 - ((p%12==5)+(p%12==7))*X^2))[12*n-11]; \\ _Amiram Eldar_, May 11 2024

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Nov 14 2019

%E More terms from _Amiram Eldar_, May 11 2024