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A275860 floor(c*s*a(n-1)) + floor(d*r*a(n-2)), where r =  (3 + sqrt(13))/2, s = r/(r-1), c = 3, d = 1, a(0) = 1, a(1) = 1. 4

%I

%S 1,1,7,33,164,813,4039,20063,99665,495099,2459470,12217747,60693301,

%T 301502133,1497752387,7440286381,36960623072,183606865105,

%U 912091791531,4530938620963,22508046862781,111811749387479,555439900107962,2759222392297991,13706808258965257

%N floor(c*s*a(n-1)) + floor(d*r*a(n-2)), where r = (3 + sqrt(13))/2, s = r/(r-1), c = 3, d = 1, a(0) = 1, a(1) = 1.

%H Clark Kimberling, <a href="/A275860/b275860.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (5,0,0,-4,0,1,-1).

%F a(n) = floor(c*s*a(n-1)) + floor(d*r*a(n-2)), where r = (3 + sqrt(13))/2, s = r/(r-1), c = 3, d = 1, a(0) = 1, a(1) = 1.

%F G.f.: (1 -4*x +2*x^2 -2*x^3 +3*x^4 -3*x^5 +x^6)/(1 -5*x +4*x^4 -x^6 +x^7).

%t c = 3; 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}]

%t CoefficientList[Series[(1-4*x+2*x^2-2*x^3+3*x^4-3*x^5+x^6)/(1-5*x+4*x^4-x^6+x^7), {x,0, 50}], x] (* _G. C. Greubel_, Feb 08 2018 *)

%o (PARI) x='x+O('x^30); Vec((1-4*x+2*x^2-2*x^3+3*x^4-3*x^5+x^6)/(1-5*x +4*x^4-x^6+x^7)) \\ _G. C. Greubel_, Feb 08 2018

%o (MAGMA) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 40); Coefficients(R!((1-4*x+2*x^2-2*x^3+3*x^4-3*x^5+x^6)/(1-5*x+4*x^4-x^6+x^7))) // _G. C. Greubel_, Feb 08 2018

%Y Cf. A275856, A275857, A275858, A275859, A275861.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Aug 12 2016

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Last modified September 27 13:39 EDT 2020. Contains 337380 sequences. (Running on oeis4.)