A008457 -id:A008457 - cp's OEIS frontend

A302855 Expansion of ((1 + 2 * Sum_{k>=1} q^(k^2))^16 - 1) / 32.

1, 15, 140, 911, 4398, 16436, 49400, 124815, 279557, 582066, 1147332, 2124340, 3692390, 6160008, 10052904, 15910799, 24151410, 35732555, 52543100, 75891378, 106006432, 145588860, 200348520, 272046644, 359002903, 468778746, 615548600, 799793800, 1014602070, 1277001048

Offset: 1

Seiichi Manyama, Apr 14 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Expansion of ((1 + 2 * Sum_{k>=1} q^(k^2))^(2^m) - 1) / 2^(m + 1): A002654 (m=1), A046897 (m=2), A008457 (m=3), this sequence (m=4), A302857 (m=5).

Cf. A000152, A186690.

a(n) = A000152(n) / 32.

A373896 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.

Original entry on oeis.org

17, 47921, 415055025, 4068011664081, 40596481219349025, 405880555110153633585, 4058721509888208894731345, 40587130610718907618215585345, 405871222004868007901459647593809, 4058712135741827985063748936303681217

Offset: 0

Seiichi Manyama, Jun 21 2024

nonn

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

Cf. A008457, A341397.

a008457(n) = sumdiv(n, d, (-1)^(n-d)*d^3);
a341397(n) = 1+16*sum(k=1, n, a008457(k));
a(n) = a341397(10^n);

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

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

cp's OEIS Frontend

A302855 Expansion of ((1 + 2 * Sum_{k>=1} q^(k^2))^16 - 1) / 32.

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