Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #2 Mar 30 2012 18:37:17
%S 3,27,111,378,1356,4131,10881,29106,73500,167643,382053,849339,
%T 1754061,3605094,7330311,14094945,26980563,51481332,93965784,
%U 170910270,311155296,545970024,955201653,1676274750,2849709768,4831999623
%N A trisection of A161804: a(n) = A161804(3n+2) for n>=0.
%C G.f. of A161804 is exp( Sum_{n>=1} A002129(n) * 3*A038500(n) * q^n/n ),
%C where A002129 forms the l.g.f. of log[ Sum_{n>=0} x^(n(n+1)/2) ], and
%C A038500(n) is the highest power of 3 dividing n.
%e G.f.: T_2(q) = 3 + 27*q + 111*q^2 + 378*q^3 + 1356*q^4 + 4131*q^5 +...
%e Terms are divisible by 3:
%e A/3=[1,9,37,126,452,1377,3627,9702,24500,55881,127351,283113,...].
%o (PARI) {a(n)=local(L=sum(m=1, 3*n+2,3*3^valuation(m,3)*sumdiv(m, d, -(-1)^d*d)*x^m/m)+x*O(x^(3*n+2))); polcoeff(exp(L), 3*n+2)}
%Y Cf. A161804, other trisections: A161805 (T_0), A161806 (T_1).
%K nonn
%O 0,1
%A _Paul D. Hanna_, Jul 20 2009