A320246 Expansion of Product_{k=1..12} theta_3(q^k), where theta_3() is the Jacobi theta function.

1, 2, 2, 6, 8, 10, 22, 26, 36, 60, 78, 106, 152, 200, 252, 360, 456, 564, 770, 940, 1178, 1532, 1852, 2256, 2858, 3430, 4100, 5086, 5982, 7076, 8612, 10040, 11672, 13960, 16068, 18496, 21866, 24796, 28288, 32924, 37074, 41876, 48156, 53732, 60014, 68546, 75836, 83996

Offset: 0

Author

Seiichi Manyama, Oct 08 2018

Keywords

• nonn

Comments

Also the number of integer solutions (a_1, a_2, ... , a_12) to the equation a_1^2 + 2*a_2^2 + ... + 12*a_12^2 = n.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Crossrefs

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), A320234 (m=8), A320241 (m=9), A320242 (m=10), this sequence (m=12), A320247 (m=16).

Cf. A320067.