cp's OEIS Frontend

A275857 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) = 2.

%I A275857 #13 Nov 16 2016 13:15:07
%S A275857 1,2,6,18,56,175,548,1717,5381,16865,52859,165674,519267,1627524,
%T A275857 5101104,15988252,50111546,157063265,492279150,1542937247,4835986551,
%U A275857 15157302067,47507122597,148900291588,466694163381,1462746914806,4584648158602,14369538930774
%N A275857 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) = 2.
%H A275857 Clark Kimberling, <a href="/A275857/b275857.txt">Table of n, a(n) for n = 0..1000</a>
%H A275857 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,1,0,-1).
%F A275857 a(n) = floor(s*a(n-1)) + floor(r*a(n-2)), where r = (1+sqrt(5))/2, s = r/(r-1).
%F A275857 G.f.: (1 - 2 x + x^2 - x^3)/(1 - 4 x + 3 x^2 - x^3 + x^5).
%t A275857 c = 1; d = 1; z = 40;
%t A275857 r = (c + Sqrt[c^2 + 4 d])/2; s = r/(r - 1); a[0] = 1; a[1] = 1;
%t A275857 a[n_] := a[n] = Floor[c*s*a[n - 1]] + Floor[d*r*a[n - 2]];
%t A275857 t = Table[a[n], {n, 0, z}] (* A275856 *)
%Y A275857 Cf. A275856, A275858-A275861.
%K A275857 nonn,easy
%O A275857 0,2
%A A275857 _Clark Kimberling_, Aug 11 2016