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A143242
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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))).
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1
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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
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OFFSET
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0,157
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COMMENTS
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|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
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LINKS
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FORMULA
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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))).
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EXAMPLE
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1 + q + q^3 + q^4 + q^6 + q^9 + q^12 + q^13 + q^16 + q^21 + q^24 + q^25 + ...
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MAPLE
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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):
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PROG
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(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))}
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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