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A289922 Coefficients of 1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r = 19/21.

%I A289922 #15 Jul 21 2017 03:25:41
%S A289922 1,2,1,0,0,0,0,0,0,0,1,3,3,1,0,0,0,0,0,0,1,3,3,1,0,0,0,0,0,0,1,2,-1,
%T A289922 -5,-4,-1,0,0,0,0,1,1,-6,-15,-14,-6,-1,0,0,0,1,0,-10,-21,-18,-7,-1,0,
%U A289922 0,0,1,-1,-13,-20,-3,18,18,7,1,0,1,-2,-15,-13,29
%N A289922 Coefficients of 1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r = 19/21.
%H A289922 Ray Chandler, <a href="/A289922/b289922.txt">Table of n, a(n) for n = 0..10000</a>
%H A289922 <a href="/index/Rec#order_21">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, -1, -1).
%F A289922 G.f.: 1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r = 19/21.
%F A289922 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 + x^20 + x^21). - _Colin Barker_, Jul 20 2017
%t A289922 z = 2000; r = 19/21;
%t A289922 CoefficientList[Series[1/Sum[Floor[1 + (k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}],
%t A289922   x];
%o A289922 (PARI) Vec((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 + x^20 + x^21) + O(x^100)) \\ _Colin Barker_, Jul 21 2017
%Y A289922 Cf. A078140 (includes guide to related sequences), A289921, A289923.
%K A289922 easy,sign
%O A289922 0,2
%A A289922 _Clark Kimberling_, Jul 18 2017