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Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 8/5.
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%I #19 Jul 16 2017 16:34:47

%S 1,-3,5,-9,17,-30,52,-90,154,-262,446,-758,1286,-2182,3702,-6278,

%T 10646,-18054,30614,-51910,88022,-149254,253078,-429126,727638,

%U -1233798,2092054,-3547334,6014934,-10199046,17293718,-29323590,49721686,-84309126,142956310

%N Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 8/5.

%C If n > 4, then a(n) is even.

%H Clark Kimberling, <a href="/A279780/b279780.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-2,-1,-2,-2).

%F G.f.: 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 8/5.

%F G.f.: (1 - x) (1 - x^5)/(1 + 2 x + x^2 + 2 x^3 + 2 x^4).

%t z = 50; f[x_] := f[x] = Sum[Floor[(8/5)*(k + 1)] x^k, {k, 0, z}]; f[x]

%t CoefficientList[Series[1/f[x], {x, 0, z}], x]

%Y Cf. A279634, A279778, A279779, A279781, A289260.

%K sign,easy

%O 0,2

%A _Clark Kimberling_, Dec 18 2016