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A289260 Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-...); [ ]=floor, r=8/5.

%I A289260 #25 Oct 13 2023 18:48:03
%S A289260 1,3,5,9,17,30,52,90,154,262,446,758,1286,2182,3702,6278,10646,18054,
%T A289260 30614,51910,88022,149254,253078,429126,727638,1233798,2092054,
%U A289260 3547334,6014934,10199046,17293718,29323590,49721686,84309126,142956310,242399686,411017942
%N A289260 Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-...); [ ]=floor, r=8/5.
%C A289260 Conjecture: the sequence is strictly increasing.
%H A289260 Colin Barker, <a href="/A289260/b289260.txt">Table of n, a(n) for n = 0..1000</a>
%H A289260 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,-2).
%F A289260 G.f.: 1/(Sum_{k>=0} [(k+1)*r](-x)^k), where r = 8/5 and [ ] = floor.
%F A289260 From _Colin Barker_, Jul 14 2017: (Start)
%F A289260 G.f.: (1 + x)^2*(1 - x + x^2 - x^3 + x^4) / ((1 - x)*(1 - x - 2*x^3)).
%F A289260 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 2*a(n-4) for n>3.
%F A289260 (End)
%F A289260 a(n) = abs(A279780(n)). - _Alois P. Heinz_, Jul 15 2017
%t A289260 r = 8/5;
%t A289260 u = 1000; (* # initial terms from given series *)
%t A289260 v = 100;   (* # coefficients in reciprocal series *)
%t A289260 CoefficientList[Series[1/Sum[Floor[r*(k + 1)] (-x)^k, {k, 0, u}], {x, 0, v}], x]
%t A289260 LinearRecurrence[{2,-1,2,-2},{1,3,5,9,17,30,52},40] (* _Harvey P. Dale_, Oct 13 2023 *)
%o A289260 (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
%Y A289260 Cf. A078140 (includes guide to related sequences), A289265.
%Y A289260 Cf. A279780.
%K A289260 nonn,easy
%O A289260 0,2
%A A289260 _Clark Kimberling_, Jul 14 2017