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

3, 30, 141, 513, 1815, 5727, 15882, 42417, 108165, 255831, 585258, 1302966, 2762349, 5705829, 11577633, 22708053, 43675938, 83011398, 153929484, 281210994, 509494515, 905832642, 1591395774, 2778237765, 4776943011

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_1(q) = 3 + 30*q + 141*q^2 + 513*q^3 + 1815*q^4 + 5727*q^5 +...
Terms are divisible by 3:
A/3=[1,10,47,171,605,1909,5294,14139,36055,85277,195086,434322,...].
		

Crossrefs

Cf. A161804, other trisections: A161805 (T_0), A161807 (T_2).

Programs

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)}