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.

1, 2, 6, 18, 56, 175, 548, 1717, 5381, 16865, 52859, 165674, 519267, 1627524, 5101104, 15988252, 50111546, 157063265, 492279150, 1542937247, 4835986551, 15157302067, 47507122597, 148900291588, 466694163381, 1462746914806, 4584648158602, 14369538930774

Offset: 0

Author

Clark Kimberling, Aug 11 2016

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-3,1,0,-1).

Crossrefs

Cf. A275856, A275858-A275861.

Programs

Mathematica

c = 1; d = 1; z = 40;
r = (c + Sqrt[c^2 + 4 d])/2; s = r/(r - 1); a[0] = 1; a[1] = 1;
a[n_] := a[n] = Floor[c*s*a[n - 1]] + Floor[d*r*a[n - 2]];
t = Table[a[n], {n, 0, z}] (* A275856 *)

Formula

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

G.f.: (1 - 2 x + x^2 - x^3)/(1 - 4 x + 3 x^2 - x^3 + x^5).