%I A098151
%S A098151 1,2,4,6,10,16,24,36,52,74,104,144,198,268,360,480,634,832,1084,1404,
%T A098151 1808,2316,2952,3744,4728,5946,7448,9294,11556,14320,17688,21780,26740,
%U A098151 32736,39968,48672,59122,71644,86616,104484,125768,151072,181104,216684
%N A098151 Number of partitions of 2n prime to 3 with all odd parts occurring with 
               even multiplicities. There is no restriction on the even parts.
%C A098151 G.f. A(x) satisfies 0=f(A(x),A(x^3)) where f(u,v)=u^3-v+3uv^2-3u^2v^3. 
               Michael Somos Dec 04 2004
%C A098151 Expansion of eta(q^2)eta(q^3)^2/(eta(q)^2eta(q^6)) in powers of q.
%D A098151 Noureddine Chair, Partition Identities From Partial Supersymmetry, to 
               be submitted
%F A098151 Euler transform of period 6 sequence [2, 1, 0, 1, 2, 0, ...]. - Vladeta 
               Jovovic (vladeta(AT)eunet.rs), Sep 24 2004
%F A098151 Taylor series of product_{k=1..inf}(1+x^k+x^(2*k))/(1-x^k+x^(2*k))= product_{k=1..inf}(1+x^k)(1-x^(3k))/
               ((1-x^k)(1+x^(3k)))=Theta_4(0, x^3)/theta_4(0, x)
%e A098151 E.g a(4)=10 because 8=4+4=4+2+2=2+2+2+2=2+2+2+1+1=2+2+1+1+1+1=4+2+1+1=4+1+1+1+1=2+1+1+1+1=1+1+1+1+1+1+1+1=...\
               
%p A098151 series(product((1+x^k+x^(2*k))/(1-x^k+x^(2*k)),k=1..150),x=0,100);
%o A098151 (PARI) a(n)=local(A); if(n<0,0, A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^3+A)^2/
               eta(x+A)^2/eta(x^6+A),n)) /* Michael Somos Dec 04 2004 */
%Y A098151 Cf. A015128.
%Y A098151 Sequence in context: A073150 A132212 A137414 this_sequence A132002 A028445 
               A006305
%Y A098151 Adjacent sequences: A098148 A098149 A098150 this_sequence A098152 A098153 
               A098154
%K A098151 nonn
%O A098151 0,2
%A A098151 Noureddine Chair (n.chair(AT)rocketmail.com), Aug 29 2004