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A275860 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.

%I A275860 #24 Sep 18 2024 12:54:10
%S A275860 1,1,7,33,164,813,4039,20063,99665,495099,2459470,12217747,60693301,
%T A275860 301502133,1497752387,7440286381,36960623072,183606865105,
%U A275860 912091791531,4530938620963,22508046862781,111811749387479,555439900107962,2759222392297991,13706808258965257
%N A275860 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.
%H A275860 Clark Kimberling, <a href="/A275860/b275860.txt">Table of n, a(n) for n = 0..1000</a>
%H A275860 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (5,0,0,-4,0,1,-1).
%F A275860 a(n) = floor(c*s*a(n-1)) + floor(d*r*a(n-2)), where r =  (3 + sqrt(13))/2 (A098316), s = r/(r-1), c = 3, d = 1, a(0) = 1, a(1) = 1.
%F A275860 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 A275860 c = 3; d = 1; z = 40;
%t A275860 r = (c + Sqrt[c^2 + 4 d])/2; s = r/(r - 1); a[0] = 1; a[1] = 1;
%t A275860 a[n_] := a[n] = Floor[c*s*a[n - 1]] + Floor[d*r*a[n - 2]];
%t A275860 t = Table[a[n], {n, 0, z}]
%t A275860 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 *)
%t A275860 LinearRecurrence[{5,0,0,-4,0,1,-1},{1,1,7,33,164,813,4039},30] (* _Harvey P. Dale_, Sep 17 2024 *)
%o A275860 (PARI) my(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 A275860 (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 A275860 Cf. A098316, A275856, A275857, A275858, A275859, A275861.
%K A275860 nonn,easy
%O A275860 0,3
%A A275860 _Clark Kimberling_, Aug 12 2016