A320240 Expansion of theta_3(q) * theta_3(q^3) * theta_3(q^5) * theta_3(q^7), where theta_3() is the Jacobi theta function.

1, 2, 0, 2, 6, 2, 4, 6, 8, 14, 4, 12, 18, 12, 12, 8, 34, 12, 8, 32, 10, 28, 0, 16, 44, 18, 16, 14, 54, 8, 12, 48, 32, 52, 28, 32, 42, 40, 8, 44, 92, 28, 16, 56, 28, 30, 44, 12, 86, 74, 8, 32, 72, 24, 40, 104, 72, 56, 32, 56, 56, 112, 8, 38, 166, 24, 36, 40, 56, 88, 52

Offset

0,2

Comments

Also the number of integer solutions (a_1, a_2, a_3, a_4) to the equation a_1^2 + 3*a_2^2 + 5*a_3^2 + 7*a_4^2 = 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^(2*k-1)): A000122 (m=1), A033716 (m=2), A320239 (m=3), this sequence (m=4).

Cf. A320078.

Sequence in context: A320239 A033727 A033757 * A320992 A320078 A136426

Adjacent sequences: A320237 A320238 A320239 * A320241 A320242 A320243

Keyword

nonn

Author

Seiichi Manyama, Oct 08 2018

Status

approved