A320248 Expansion of Product_{k=1..24} 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, 202, 258, 370, 478, 602, 828, 1042, 1332, 1758, 2198, 2758, 3572, 4446, 5512, 7002, 8614, 10616, 13292, 16260, 19792, 24496, 29724, 35976, 44062, 52992, 63780, 77296, 92518, 110532, 132848, 158036, 187674, 224066, 264960

Offset

0,2

Comments

Also the number of integer solutions (a_1, a_2, ... , a_24) to the equation a_1^2 + 2*a_2^2 + ... + 24*a_24^2 = n.

a(24045) = 45676735553670596752038069309732400 and a(24046) = 45676724028345437854371347712212432. So a(24045) > a(24046).

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), A320246 (m=12), A320247 (m=16), this sequence (m=24).

Cf. A320067.

Sequence in context: A320242 A320246 A320247 * A320067 A248823 A284616

Adjacent sequences: A320245 A320246 A320247 * A320249 A320250 A320251

Keyword

nonn

Author

Seiichi Manyama, Oct 08 2018

Status

approved