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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.)