A289914 Coefficients of 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = 7/5.

1, 3, 5, 9, 18, 35, 66, 124, 234, 441, 830, 1563, 2944, 5544, 10440, 19661, 37026, 69727, 131310, 247284, 465686, 876981, 1651534, 3110175, 5857092, 11030096, 20771916, 39117745, 73666674, 138729339, 261255578, 491997420, 926531266, 1744846929, 3285901854

Offset

0,2

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,-1,2,-1).

Formula

G.f.: 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = 7/5.

From Colin Barker, Jul 19 2017: (Start)

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

a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - a(n-4) for n>3.

(End)

Mathematica

z = 2000; r = 7/5;
u = CoefficientList[Series[1/Sum[Round[(k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}],
  x];  (* A289914  *)
v = N[u[[z]]/u[[z - 1]], 200]
RealDigits[v, 10][[1]] (* A289915 *)

Prog

(PARI) Vec((1+x)^2*(1-x+x^2-x^3+x^4) / (1-2*x+x^2-2*x^3+x^4) + O(x^50)) \\ Colin Barker, Jul 20 2017

Crossrefs

Cf. A078140 (includes guide to related sequences), A289915.

Sequence in context: A120941 A108227 A289912 * A251704 A288230 A289262

Adjacent sequences: A289911 A289912 A289913 * A289915 A289916 A289917

Keyword

nonn,easy

Author

Clark Kimberling, Jul 18 2017

Status

approved