%I #21 Jul 05 2019 19:06:13

%S 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 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 32,176,416,552,450,231,73,13,1,0,64,384,1008

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

%C Conjecture: all the terms are nonnegative.

%H Ray Chandler, <a href="/A289921/b289921.txt">Table of n, a(n) for n = 0..10000</a>

%H Milan Janjić, <a href="https://arxiv.org/abs/1905.04465">On Restricted Ternary Words and Insets</a>, arXiv:1905.04465 [math.CO], 2019.

%H <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 G.f.: 1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r = 9/10.

%F 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 z = 2000; r = 9/10;

%t CoefficientList[Series[1/Sum[Floor[1 + (k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}],

%t x];

%o (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 Cf. A078140 (includes guide to related sequences), A289922, A289923.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jul 18 2017