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A275856 a(n) = floor(c*s*a(n-1)) + floor(d*r*a(n-2)), where r = (1+sqrt(5))/2, s = r/(r-1), c = 1, d = 1, a(0) = 1, a(1) = 1.

%I A275856 #15 Mar 21 2025 17:31:51
%S A275856 1,1,3,8,24,74,231,723,2265,7098,22246,69724,218533,684941,2146791,
%T A275856 6728628,21089356,66099798,207174811,649342415,2035216397,6378923798,
%U A275856 19993288618,62664424664,196407414185,615594454969,1929441078187,6047395073408,18954187089376
%N A275856 a(n) = floor(c*s*a(n-1)) + floor(d*r*a(n-2)), where r = (1+sqrt(5))/2, s = r/(r-1), c = 1, d = 1, a(0) = 1, a(1) = 1.
%H A275856 Clark Kimberling, <a href="/A275856/b275856.txt">Table of n, a(n) for n = 0..1000</a>
%H A275856 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,1,0,-1).
%F A275856 a(n) = floor(s*a(n-1)) + floor(r*a(n-2)), where r = (1+sqrt(5))/2, s = r/(r-1).
%F A275856 G.f.: (1 - 3 x + 2 x^2 - 2 x^3)/(1 - 4 x + 3 x^2 - x^3 + x^5).
%t A275856 c = 1; d = 1; z = 40;
%t A275856 r = (c + Sqrt[c^2 + 4 d])/2; s = r/(r - 1); a[0] = 1; a[1] = 1;
%t A275856 a[n_] := a[n] = Floor[c*s*a[n - 1]] + Floor[d*r*a[n - 2]];
%t A275856 t = Table[a[n], {n, 0, z}]
%t A275856 LinearRecurrence[{4,-3,1,0,-1},{1,1,3,8,24},40] (* _Harvey P. Dale_, Mar 21 2025 *)
%Y A275856 Cf. A275857-A275861.
%K A275856 nonn,easy
%O A275856 0,3
%A A275856 _Clark Kimberling_, Aug 11 2016