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A275638
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Expansion of (1-q)^k/Product_{j=1..k} (1-q^j) for k=4.
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8
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1, -3, 4, -3, 2, -3, 5, -6, 6, -6, 6, -6, 7, -9, 10, -9, 8, -9, 11, -12, 12, -12, 12, -12, 13, -15, 16, -15, 14, -15, 17, -18, 18, -18, 18, -18, 19, -21, 22, -21, 20, -21, 23, -24, 24, -24, 24, -24, 25, -27, 28, -27, 26, -27, 29, -30, 30, -30, 30, -30, 31, -33, 34, -33, 32, -33, 35, -36, 36
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OFFSET
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0,2
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LINKS
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FORMULA
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Equivalent g.f.: 1 / ((1+x)^2*(1+x^2)*(1+x+x^2)). - Colin Barker, Aug 10 2016
a(n) = -3*a(n-1) - 5*a(n-2) - 6*a(n-3) - 5*a(n-4) - 3*a(n-5) - a(n-6).
a(n) = (sqrt(3)*(-1)^n*n + 3*sqrt(3)*(-1)^n - 4*sin(2*Pi n/3) - sqrt(3)*cos(Pi*n/2))/(2*sqrt(3)). (End)
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MAPLE
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f1:=k->(1-q)^k/mul(1-q^i, i=1..k);
f2:=k->series(f1(k), q, 75);
f3:=k->seriestolist(f2(k));
f3(4);
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PROG
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(PARI) Vec(1/((1+x)^2*(1+x^2)*(1+x+x^2)) + O(x^100)) \\ Colin Barker, Aug 11 2016
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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