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 A279634 Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 3/2. 9
 1, -3, 5, -9, 18, -36, 72, -144, 288, -576, 1152, -2304, 4608, -9216, 18432, -36864, 73728, -147456, 294912, -589824, 1179648, -2359296, 4718592, -9437184, 18874368, -37748736, 75497472, -150994944, 301989888, -603979776, 1207959552, -2415919104, 4831838208 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS After first 3 terms, agrees with A005010 except for signs; in particular 9 divides a(n) for n >= 3. Suppose r = c/d is a rational number and (a(n)) is the coefficient series for 1/([r] + [2r]x + [3r]x^2 + ...). Let (s(k)) be the increasing sequence of indices n(k) for which a(n(k)) > = 0. In the table below, "yes" indicates that a check of the first 1000 terms indicates that (n(k)) is (eventually) periodic. Column 1 gives selected values of r, and column 2 gives the corresponding coefficient series. 3/2    A279634     yes 4/3    A279675     no 5/3    A279676     no 5/4    A279677     yes 7/4    A279678     yes 6/5    A279778     no 7/5    A279779     no 8/5    A279780     yes 9/5    A279781     no LINKS Clark Kimberling, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (-2). FORMULA G.f.: 1/(1 + 3x + 4x^2 + 6x^3 + ...). G.f.: (1 - x) (1 - x^2)/(1 + 2x). MATHEMATICA z = 50; f[x_] := f[x] = Sum[Floor[(3/2)*(k + 1)] x^k, {k, 0, z}]; f[x] CoefficientList[Series[1/f[x], {x, 0, z}], x] CROSSREFS Cf. A005010. Sequence in context: A288229 A293332 A288135 * A028411 A018098 A108859 Adjacent sequences:  A279631 A279632 A279633 * A279635 A279636 A279637 KEYWORD sign,easy AUTHOR Clark Kimberling, Dec 18 2016 STATUS approved

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Last modified September 19 07:24 EDT 2020. Contains 337178 sequences. (Running on oeis4.)