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A320248
Expansion of Product_{k=1..24} theta_3(q^k), where theta_3() is the Jacobi theta function.
1
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
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 08 2018
STATUS
approved