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A289923 Limiting sequence of coefficients of 1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r approaches 19/21 from the left.

%I A289923 #14 Jul 22 2017 11:45:24
%S A289923 1,2,1,0,0,0,0,0,0,0,1,3,3,1,0,0,0,0,0,0,2,7,9,5,1,0,0,0,0,0,3,12,19,
%T A289923 15,6,1,0,0,0,0,5,22,40,39,22,7,1,0,0,0,8,39,81,94,67,30,8,1,0,0,13,
%U A289923 69,160,214,183,104,39,9,1,0,21,121,310,468,464
%N A289923 Limiting sequence of coefficients of 1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r approaches 19/21 from the left.
%C A289923 Conjecture:  all the terms are nonnegative.
%H A289923 Ray Chandler, <a href="/A289923/b289923.txt">Table of n, a(n) for n = 0..10000</a>
%H A289923 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (1, -1, 1, -1, 1, -1, 1, -1, 1, 0, 1, -1, 1, -1, 1, -1, 1, -1, 1).
%F A289923 G.f.:  1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r = 19/21-10^(-9).
%F A289923 G.f.: (1 + x)^2*(1 - x + x^2)*(1 - x + x^2 - x^3 + x^4 - x^5 + x^6)*(1 + x - x^3 - x^4 + x^6 - x^8 - x^9 + x^11 + x^12) / (1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 - x^11 + x^12 - x^13 + x^14 - x^15 + x^16 - x^17 + x^18 - x^19). - _Colin Barker_, Jul 20 2017
%t A289923 z = 2000; r = 19/21-10^(-9);
%t A289923 CoefficientList[Series[1/Sum[Floor[1 + (k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}],
%t A289923   x];
%Y A289923 Cf. A078140 (includes guide to related sequences), A289921, A289922.
%K A289923 nonn,easy
%O A289923 0,2
%A A289923 _Clark Kimberling_, Jul 18 2017