A289916 Coefficients of 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = 9/7.

1, 3, 5, 8, 13, 22, 39, 69, 120, 206, 353, 607, 1046, 1803, 3106, 5348, 9208, 15856, 27306, 47025, 80982, 139457, 240155, 413566, 712196, 1226463, 2112073, 3637166, 6263503, 10786276, 18574872, 31987488, 55085136, 94861220, 163358969, 281317834, 484452887

Offset: 0

Author

Clark Kimberling, Jul 18 2017

Keywords

• nonn
• easy

Comments

Conjecture: the sequence is strictly increasing.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-1,2,-1).

Crossrefs

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

Programs

Mathematica

z = 2000; r = 9/7;
u = CoefficientList[Series[1/Sum[Round[(k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}],
  x];  (* A289916  *)
v = N[u[[z]]/u[[z - 1]], 200]
RealDigits[v, 10][[1]] (* A289917 *)

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

Formula

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

From Colin Barker, Jul 19 2017: (Start)

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)).

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.

(End)