cp's OEIS Frontend

A161806 A trisection of A161804: a(n) = A161804(3n+1) for n>=0.

%I A161806 #2 Mar 30 2012 18:37:17
%S A161806 3,30,141,513,1815,5727,15882,42417,108165,255831,585258,1302966,
%T A161806 2762349,5705829,11577633,22708053,43675938,83011398,153929484,
%U A161806 281210994,509494515,905832642,1591395774,2778237765,4776943011
%N A161806 A trisection of A161804: a(n) = A161804(3n+1) for n>=0.
%C A161806 G.f. of A161804 is exp( Sum_{n>=1} A002129(n) * 3*A038500(n) * q^n/n ),
%C A161806 where A002129 forms the l.g.f. of log[ Sum_{n>=0} x^(n(n+1)/2) ], and
%C A161806 A038500(n) is the highest power of 3 dividing n.
%e A161806 G.f.: T_1(q) = 3 + 30*q + 141*q^2 + 513*q^3 + 1815*q^4 + 5727*q^5 +...
%e A161806 Terms are divisible by 3:
%e A161806 A/3=[1,10,47,171,605,1909,5294,14139,36055,85277,195086,434322,...].
%o A161806 (PARI) {a(n)=local(L=sum(m=1, 3*n+1,3*3^valuation(m,3)*sumdiv(m, d, -(-1)^d*d)*x^m/m)+x*O(x^(3*n+1))); polcoeff(exp(L), 3*n+1)}
%Y A161806 Cf. A161804, other trisections: A161805 (T_0), A161807 (T_2).
%K A161806 nonn
%O A161806 0,1
%A A161806 _Paul D. Hanna_, Jul 20 2009