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A320234 Expansion of Product_{k=1..8} theta_3(q^k), where theta_3() is the Jacobi theta function. 10

%I

%S 1,2,2,6,8,10,22,26,36,58,72,96,130,164,200,268,324,376,486,552,642,

%T 796,876,992,1198,1294,1436,1682,1794,1964,2268,2428,2556,2980,3116,

%U 3304,3876,3940,4252,4896,4996,5348,6164,6260,6668,7686,7808,8120,9378,9490,9762

%N Expansion of Product_{k=1..8} theta_3(q^k), where theta_3() is the Jacobi theta function.

%C Also the number of integer solutions (a_1, a_2, ... , a_8) to the equation a_1^2 + 2*a_2^2 + ... + 8*a_8^2 = n.

%H Seiichi Manyama, <a href="/A320234/b320234.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>

%Y Product_{k=1..m} theta_3(q^k): A000122 (m=1), A033715 (m=2), A029594 (m=3), A320139 (m=4), A320231 (m=5), A320232 (m=6), A320233 (m=7), this sequence (m=8), A320241 (m=9), A320242(m=10), A320246 (m=12), A320247 (m=16).

%Y Cf. A320067, A320243.

%K nonn,look

%O 0,2

%A _Seiichi Manyama_, Oct 08 2018

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Last modified February 25 22:55 EST 2020. Contains 332270 sequences. (Running on oeis4.)