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%I #18 Nov 04 2015 03:46:55
%S 1,4,14,28,57,84,148,196,312,364,546,624,910,988,1352,1456,1974,2072,
%T 2710,2800,3705,3724,4816,4788,6188,6076,7658,7644,9620,9352,11536,
%U 11284,14183,13468,16542,15996,19864,18928,22820,21904,26880,25284
%N Theta series of A2[hole]^4.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 111, Eq (63)^4.
%F a(n) = A033685^4.
%F Expansion of q^(-4/3) * (eta(q^3)^3 / eta(q))^4 in powers of q. - _Michael Somos_, Aug 22 2007
%F Expansion of c(q)^4 / (81 * q^(4/3)) in powers of q where c() is a cubic AGM function. - _Michael Somos_, Aug 22 2007
%F Euler transform of period 3 sequence [ 4, 4, -8, ...]. - _Michael Somos_, Aug 22 2007
%F A092342(n) = A000731(n) + 81*a(n-1). - _Michael Somos_, Aug 22 2007
%e q^4 + 4*q^7 + 14*q^10 + 28*q^13 + 57*q^16 + 84*q^19 + 148*q^22 + ...
%t s = (QPochhammer[q^3]^3/QPochhammer[q])^4 + O[q]^45; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 04 2015 *)
%o (PARI) {a(n) = local(A); if(n<0, 0, A = x*O(x^n); polcoeff( (eta(x^3 +A)^3 / eta(x +A) )^4, n))} /* _Michael Somos_, Aug 22 2007 */
%Y Cf. A033685.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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