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A288237
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Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-...); [ ]=floor, r=sqrt(11/4).
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3
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1, 3, 5, 9, 17, 30, 52, 91, 160, 281, 493, 865, 1518, 2664, 4675, 8204, 14397, 25265, 44337, 77806, 136540, 239611, 420488, 737905, 1294933, 2272449, 3987870, 6998224, 12281027, 21551700, 37820597, 66370521, 116472145, 204394366, 358687108, 629451995
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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 = sqrt(11/4) and [ ] = floor.
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MAPLE
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N:= 100: # to get a(0)..a(N)
r:= sqrt(11/4):
G:= 1/add(floor((k+1)*r)*(-x)^k, k=0..N):
S:= series(G, x, N+1):
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MATHEMATICA
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r = Sqrt[11/4];
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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CROSSREFS
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Cf. A078140 (includes guide to related sequences).
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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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