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Number of lattice points inside or on the 8-dimensional hypersphere x_1^2 + x_2^2 + x_3^2 + x_4^2 + x_5^2 + x_6^2 + x_7^2 + x_8^2 = 10^n.
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%I #14 Jun 21 2024 10:47:19

%S 17,47921,415055025,4068011664081,40596481219349025,

%T 405880555110153633585,4058721509888208894731345,

%U 40587130610718907618215585345,405871222004868007901459647593809,4058712135741827985063748936303681217

%N Number of lattice points inside or on the 8-dimensional hypersphere x_1^2 + x_2^2 + x_3^2 + x_4^2 + x_5^2 + x_6^2 + x_7^2 + x_8^2 = 10^n.

%F a(n) = A341397(10^n).

%F a(n) == 1 (mod 16).

%o (PARI) a008457(n) = sumdiv(n, d, (-1)^(n-d)*d^3);

%o a341397(n) = 1+16*sum(k=1, n, a008457(k));

%o a(n) = a341397(10^n);

%Y Cf. A068785, A373881, A373882, A373883, A373884, A373885.

%Y Cf. A008457, A341397.

%K nonn

%O 0,1

%A _Seiichi Manyama_, Jun 21 2024