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A373882
Number of lattice points inside or on the 4-dimensional hypersphere x^2 + y^2 + z^2 + u^2 = 10^n.
6
9, 569, 49689, 4937225, 493490641, 49348095737, 4934805110729, 493480252693889, 49348022079085897, 4934802199975704129, 493480220066583590433, 49348022005552308828457, 4934802200546833521392241, 493480220054489318828539601, 49348022005446802425711456713, 4934802200544679211736756034457
OFFSET
0,1
FORMULA
a(n) = A046895(10^n).
a(n) == 1 (mod 8).
Limit_{n->oo} a(n) = Pi^2*100^n/2. - Hugo Pfoertner, Jun 21 2024
PROG
(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);
a(n) = b(4, 10^n);
(Python)
from math import isqrt
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 21 2024
STATUS
approved