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A289262
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Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-...); [ ]=floor, r=11/7.
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2
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1, 3, 5, 9, 18, 36, 71, 138, 268, 522, 1017, 1980, 3853, 7498, 14594, 28406, 55287, 107604, 209429, 407614, 793344, 1544090, 3005269, 5849172, 11384281, 22157298, 43124882, 83934214, 163361667, 317951804, 618831521, 1204435526, 2344200136, 4562530890
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OFFSET
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0,2
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COMMENTS
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Conjecture: the sequence is strictly increasing.
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LINKS
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FORMULA
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G.f.: 1/(Sum_{k>=0} [(k+1)*r)](-x)^k), where r = 11/7 and [ ] = floor.
G.f.: (1 + x)^2*(1 - x + x^2 - x^3 + x^4 - x^5 + x^6) / (1 - 2*x + x^2 - 2*x^3 + x^4 - 2*x^5 + 2*x^6). - Colin Barker, Jul 14 2017
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MATHEMATICA
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r = 11/7;
u = 1000; (* # initial terms from given series *)
v = 100; (* # coefficients in reciprocal series *)
CoefficientList[Series[1/Sum[Floor[r*(k + 1)] (-x)^k, {k, 0, u}], {x, 0, v}], x]
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PROG
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(PARI) Vec((1 + x)^2*(1 - x + x^2 - x^3 + x^4 - x^5 + x^6) / (1 - 2*x + x^2 - 2*x^3 + x^4 - 2*x^5 + 2*x^6) + O(x^50)) \\ Colin Barker, Jul 20 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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