cp's OEIS Frontend

A373882 Number of lattice points inside or on the 4-dimensional hypersphere x^2 + y^2 + z^2 + u^2 = 10^n.

%I A373882 #33 Jun 21 2024 10:24:32
%S A373882 9,569,49689,4937225,493490641,49348095737,4934805110729,
%T A373882 493480252693889,49348022079085897,4934802199975704129,
%U A373882 493480220066583590433,49348022005552308828457,4934802200546833521392241,493480220054489318828539601,49348022005446802425711456713,4934802200544679211736756034457
%N A373882 Number of lattice points inside or on the 4-dimensional hypersphere x^2 + y^2 + z^2 + u^2 = 10^n.
%H A373882 Wikipedia, <a href="https://en.wikipedia.org/wiki/Jacobi%27s_four-square_theorem">Jacobi four square theorem</a>
%F A373882 a(n) = A046895(10^n).
%F A373882 a(n) == 1 (mod 8).
%F A373882 Limit_{n->oo} a(n) = Pi^2*100^n/2. - _Hugo Pfoertner_, Jun 21 2024
%o A373882 (PARI) b(k, n) = my(q='q+O('q^(n+1))); polcoef((eta(q^2)^5/(eta(q)^2*eta(q^4)^2))^k/(1-q), n);
%o A373882 a(n) = b(4, 10^n);
%o A373882 (Python)
%o A373882 from math import isqrt
%o A373882 def A373882(n): return 1+((-(s:=isqrt(a:=10**n))**2*(s+1)+sum((q:=a//k)*((k<<1)+q+1) for k in range(1,s+1))&-1)<<2)+(((t:=isqrt(m:=a>>2))**2*(t+1)-sum((q:=m//k)*((k<<1)+q+1) for k in range(1,t+1))&-1)<<4) # _Chai Wah Wu_, Jun 21 2024
%Y A373882 Cf. A068785, A373881, A373883, A373884, A373885.
%Y A373882 Cf. A024916, A046895.
%K A373882 nonn
%O A373882 0,1
%A A373882 _Seiichi Manyama_, Jun 21 2024