A275858 - OEIS

%I #15 Sep 08 2022 08:46:17

%S 1,1,-1,-4,-4,4,17,17,-17,-72,-72,72,305,305,-305,-1292,-1292,1292,

%T 5473,5473,-5473,-23184,-23184,23184,98209,98209,-98209,-416020,

%U -416020,416020,1762289,1762289,-1762289,-7465176,-7465176,7465176,31622993,31622993

%N 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.

%H Clark Kimberling, <a href="/A275858/b275858.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,-2,-1,-1).

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

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

%t c = 1; d = 1; z = 40;

%t r = (c + Sqrt[c^2 + 4 d])/2; s = r/(r - 1); a[0] = 1; a[1] = 1;

%t a[n_] := a[n] = Floor[c*s*a[n - 1]] + Floor[d*r*a[n - 2]];

%t t = Table[a[n], {n, 0, z}] (* A275856 *)

%t CoefficientList[Series[1/(1-x+2*x^2+x^3+x^4), {x,0, 50}], x] (* _G. C. Greubel_, Feb 08 2018 *)

%o (PARI) x='x+O('x^30); Vec(1/(1-x+2*x^2+x^3+x^4)) \\ _G. C. Greubel_, Feb 08 2018

%o (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

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

%K easy,sign

%O 0,4

%A _Clark Kimberling_, Aug 12 2016