A008433 - OEIS

%I #33 Feb 16 2025 08:32:32

%S 1,0,0,0,0,16,0,0,40,0,0,0,0,80,0,0,90,0,0,0,0,160,0,0,240,0,0,0,0,

%T 240,0,0,200,0,0,0,0,400,0,0,560,0,0,0,0,496,0,0,400,0,0,0,0,560,0,0,

%U 800,0,0,0,0,880,0,0,730

%N Theta series of {D_5}^{+} packing.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.

%H Seiichi Manyama, <a href="/A008433/b008433.txt">Table of n, a(n) for n = 0..10000</a>

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

%F From _Seiichi Manyama_, Oct 21 2018: (Start)

%F Expansion of (theta_2(q)^5 + theta_3(q)^5 + theta_4(q)^5)/2 in powers of q^(1/4).

%F Expansion of (Sum_{k=-oo..oo} q^((k+1/2)^2))^5 + (Sum_{k=-oo..oo} q^(k^2))^5 + (Sum_{k=-oo..oo} (-1)^k * q^(k^2))^5 in powers of q^(1/4). (End)

%e G.f.: 1 + 16*q^(5/4) + 40*q^2 + 80*q^(13/4) + 90*q^4 + ... .

%Y Cf. A000122 (theta_3(q)), A002448 (theta_4(q)), A005930.

%K nonn,easy

%O 0,6

%A _N. J. A. Sloane_