A275858 a(n) = floor(c*r*a(n-1)) - floor(d*s*a(n-2)), where r = (1+sqrt(5))/2, s = r/(r-1), c = 1, d = 1, a(0) = 1, a(1) = 1.

1, 1, -1, -4, -4, 4, 17, 17, -17, -72, -72, 72, 305, 305, -305, -1292, -1292, 1292, 5473, 5473, -5473, -23184, -23184, 23184, 98209, 98209, -98209, -416020, -416020, 416020, 1762289, 1762289, -1762289, -7465176, -7465176, 7465176, 31622993, 31622993

Offset

0,4

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,-2,-1,-1).

Formula

a(n) = floor(r*a(n-1)) - floor(s*a(n-2)), where r = (1+sqrt(5))/2, s = r/(r-1).

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

Mathematica

c = 1; d = 1; z = 40;
r = (c + Sqrt[c^2 + 4 d])/2; s = r/(r - 1); a[0] = 1; a[1] = 1;
a[n_] := a[n] = Floor[c*s*a[n - 1]] + Floor[d*r*a[n - 2]];
t = Table[a[n], {n, 0, z}] (* A275856 *)
CoefficientList[Series[1/(1-x+2*x^2+x^3+x^4), {x, 0, 50}], x] (* G. C. Greubel, Feb 08 2018 *)

Prog

(PARI) x='x+O('x^30); Vec(1/(1-x+2*x^2+x^3+x^4)) \\ G. C. Greubel, Feb 08 2018
(Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 40); Coefficients(R!(1/(1-x+2*x^2+x^3+x^4))) // G. C. Greubel, Feb 08 2018

Crossrefs

Cf. A275856, A275857, A275859, A275860, A275861.

Sequence in context: A231586 A231700 A231746 * A241094 A319257 A131946

Adjacent sequences: A275855 A275856 A275857 * A275859 A275860 A275861

Keyword

easy,sign

Author

Clark Kimberling, Aug 12 2016

Status

approved