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A289921
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Coefficients of 1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r = 9/10.
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3
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1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 0, 0, 2, 7, 9, 5, 1, 0, 0, 0, 0, 0, 4, 16, 25, 19, 7, 1, 0, 0, 0, 0, 8, 36, 66, 63, 33, 9, 1, 0, 0, 0, 16, 80, 168, 192, 129, 51, 11, 1, 0, 0, 32, 176, 416, 552, 450, 231, 73, 13, 1, 0, 64, 384, 1008
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OFFSET
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0,2
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COMMENTS
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Conjecture: all the terms are nonnegative.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1, -1, 1, -1, 1, -1, 1, -1, 1, 1).
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FORMULA
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G.f.: 1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r = 9/10.
G.f.: (1 - x)*(1 + x)^2*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4) / (1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 - x^10). - Colin Barker, Jul 20 2017
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MATHEMATICA
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z = 2000; r = 9/10;
CoefficientList[Series[1/Sum[Floor[1 + (k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}],
x];
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PROG
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(PARI) Vec( (1 - x)*(1 + x)^2*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4) / (1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 - x^10) + O(x^100)) \\ Colin Barker, Jul 21 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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