A289916 - OEIS

%I #11 Jul 20 2017 06:12:45

%S 1,3,5,8,13,22,39,69,120,206,353,607,1046,1803,3106,5348,9208,15856,

%T 27306,47025,80982,139457,240155,413566,712196,1226463,2112073,

%U 3637166,6263503,10786276,18574872,31987488,55085136,94861220,163358969,281317834,484452887

%N Coefficients of 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = 9/7.

%C Conjecture: the sequence is strictly increasing.

%H Colin Barker, <a href="/A289916/b289916.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-1,2,-1).

%F G.f.:  1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = 9/7.

%F From _Colin Barker_, Jul 19 2017: (Start)

%F G.f.: (1+x)^2*(1-x+x^2-x^3+x^4-x^5+x^6) / ((1-x+x^2)*(1-x-x^2-x^3+x^4)).

%F a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) + 2*a(n-5) - a(n-6) for n>5.

%F (End)

%t z = 2000; r = 9/7;

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

%t   x];  (* A289916  *)

%t v = N[u[[z]]/u[[z - 1]], 200]

%t RealDigits[v, 10][[1]] (* A289917 *)

%o (PARI) Vec((1+x)^2*(1-x+x^2-x^3+x^4-x^5+x^6) / ((1-x+x^2)*(1-x-x^2-x^3+x^4)) + O(x^50)) \\ _Colin Barker_, Jul 20 2017

%Y Cf. A078140 (includes guide to related sequences), A289917.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jul 18 2017