cp's OEIS Frontend

A289921 Coefficients of 1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r = 9/10.

%I A289921 #21 Jul 05 2019 19:06:13
%S A289921 1,2,1,0,0,0,0,0,0,0,1,3,3,1,0,0,0,0,0,0,2,7,9,5,1,0,0,0,0,0,4,16,25,
%T A289921 19,7,1,0,0,0,0,8,36,66,63,33,9,1,0,0,0,16,80,168,192,129,51,11,1,0,0,
%U A289921 32,176,416,552,450,231,73,13,1,0,64,384,1008
%N A289921 Coefficients of 1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r = 9/10.
%C A289921 Conjecture: all the terms are nonnegative.
%H A289921 Ray Chandler, <a href="/A289921/b289921.txt">Table of n, a(n) for n = 0..10000</a>
%H A289921 Milan Janjić, <a href="https://arxiv.org/abs/1905.04465">On Restricted Ternary Words and Insets</a>, arXiv:1905.04465 [math.CO], 2019.
%H A289921 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1, -1, 1, -1, 1, -1, 1, -1, 1, 1).
%F A289921 G.f.: 1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r = 9/10.
%F A289921 G.f.: (1 - x)*(1 + x)^2*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4) / (1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 - x^10). - _Colin Barker_, Jul 20 2017
%t A289921 z = 2000; r = 9/10;
%t A289921 CoefficientList[Series[1/Sum[Floor[1 + (k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}],
%t A289921   x];
%o A289921 (PARI) Vec( (1 - x)*(1 + x)^2*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4) / (1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 - x^10) + O(x^100)) \\ _Colin Barker_, Jul 21 2017
%Y A289921 Cf. A078140 (includes guide to related sequences), A289922, A289923.
%K A289921 nonn,easy
%O A289921 0,2
%A A289921 _Clark Kimberling_, Jul 18 2017