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A289260
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Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-...); [ ]=floor, r=8/5.
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3
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1, 3, 5, 9, 17, 30, 52, 90, 154, 262, 446, 758, 1286, 2182, 3702, 6278, 10646, 18054, 30614, 51910, 88022, 149254, 253078, 429126, 727638, 1233798, 2092054, 3547334, 6014934, 10199046, 17293718, 29323590, 49721686, 84309126, 142956310, 242399686, 411017942
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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 = 8/5 and [ ] = floor.
G.f.: (1 + x)^2*(1 - x + x^2 - x^3 + x^4) / ((1 - x)*(1 - x - 2*x^3)).
a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 2*a(n-4) for n>3.
(End)
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MATHEMATICA
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r = 8/5;
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]
LinearRecurrence[{2, -1, 2, -2}, {1, 3, 5, 9, 17, 30, 52}, 40] (* Harvey P. Dale, Oct 13 2023 *)
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PROG
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(PARI) Vec((1 + x)^2*(1 - x + x^2 - x^3 + x^4) / ((1 - x)*(1 - x - 2*x^3)) + 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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