A161807 A trisection of A161804: a(n) = A161804(3n+2) for n>=0.

3, 27, 111, 378, 1356, 4131, 10881, 29106, 73500, 167643, 382053, 849339, 1754061, 3605094, 7330311, 14094945, 26980563, 51481332, 93965784, 170910270, 311155296, 545970024, 955201653, 1676274750, 2849709768, 4831999623

Offset: 0

Author

Paul D. Hanna, Jul 20 2009

Keywords

• nonn

Comments

G.f. of A161804 is exp( Sum_{n>=1} A002129(n) * 3*A038500(n) * q^n/n ),

where A002129 forms the l.g.f. of log[ Sum_{n>=0} x^(n(n+1)/2) ], and

A038500(n) is the highest power of 3 dividing n.

Examples

			G.f.: T_2(q) = 3 + 27*q + 111*q^2 + 378*q^3 + 1356*q^4 + 4131*q^5 +...
Terms are divisible by 3:
A/3=[1,9,37,126,452,1377,3627,9702,24500,55881,127351,283113,...].
		

Crossrefs

Cf. A161804, other trisections: A161805 (T_0), A161806 (T_1).

Programs

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)}