A289912 Coefficients of 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = sqrt(2).

1, 3, 5, 9, 18, 35, 66, 124, 234, 441, 829, 1557, 2925, 5496, 10325, 19394, 36429, 68428, 128532, 241425, 453475, 851775, 1599910, 3005145, 5644626, 10602419, 19914742, 37406262, 70260933, 131972522, 247886635, 465610427, 874565375, 1642713630, 3085541851

Offset

0,2

Comments

Conjecture: the sequence is strictly increasing.

Links

Table of n, a(n) for n=0..34.

Formula

G.f.: 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = sqrt(2).

Mathematica

z = 100; r = Sqrt[2];
u = CoefficientList[Series[1/Sum[Round[(k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}],
  x];  (* A289912 *)
v = N[u[[z]]/u[[z - 1]], 200]
d = RealDigits[v, 10][[1]] (* A289913 *)

Crossrefs

Cf. A078140 (includes guide to related sequences), A289913.

Sequence in context: A281852 A120941 A108227 * A289914 A251704 A288230

Adjacent sequences: A289909 A289910 A289911 * A289913 A289914 A289915

Keyword

nonn,easy

Author

Clark Kimberling, Jul 18 2017

Status

approved