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Search: id:A143242
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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
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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|a(n)|<2 if n<156, |a(n)|<3 if n<250.
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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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PROGRAM
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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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Sequence in context: A077049 A124895 A089885 this_sequence A136442 A128431 A054521
Adjacent sequences: A143239 A143240 A143241 this_sequence A143243 A143244 A143245
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 01 2008
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