A143242 Expansion of Product_{k>0} (1 - x^(9*k)) * (1-x^(9*k-2)) * (1-x^(9*k-7)) / ((1-x^(9*k-1)) * (1-x^(9*k-6)) * (1-x^(9*k-8))).

1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, 1, 1, 0, 1, 1, 0, 0, -1, 0, 1, 0, 0, 1, 1, 0, -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0

Offset

0,157

Comments

|a(n)|<2 if n<156, |a(n)|<3 if n<250.

It appears that a(n) = 0 if n == 2 (mod 3). - Robert Israel, Jan 31 2018

Links

Robert Israel, Table of n, a(n) for n = 0..3000

Formula

Euler transform of period 9 sequence [ 1, -1, 1, 0, 0, 0, -1, 1, -1, ...].

G.f.: Product_{k>0} (1 - x^(9*k)) * (1-x^(9*k-2)) * (1-x^(9*k-7)) / ((1-x^(9*k-1)) * (1-x^(9*k-6)) * (1-x^(9*k-8))).

Example

1 + q + q^3 + q^4 + q^6 + q^9 + q^12 + q^13 + q^16 + q^21 + q^24 + q^25 + ...

Maple

N:= 100: # to get a(0)..a(N)
g:= mul((1 - x^(9*k)) * (1-x^(9*k-2)) * (1-x^(9*k-7)) / ((1-x^(9*k-1)) * (1-x^(9*k-6)) * (1-x^(9*k-8))), k=1..floor((N+8)/9)):
S:= series(g, x, N+1):
seq(coeff(S, x, n), n=0..N); # Robert Israel, Jan 31 2018

Prog

(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k)^([1, -1, 1, -1, 0, 0, 0, 1, -1][k%9 + 1]), 1 + x * O(x^n)), n))}

Crossrefs

Sequence in context: A124895 A089885 A190233 * A136442 A168030 A128431

Adjacent sequences: A143239 A143240 A143241 * A143243 A143244 A143245

Keyword

sign,look

Author

Michael Somos, Aug 01 2008

Status

approved