A272123 a(n) = Fibonacci(3n) - Fibonacci(2n).

0, 1, 5, 26, 123, 555, 2440, 10569, 45381, 193834, 825275, 3506867, 14883984, 63124593, 267596485, 1134071130, 4805348667, 20359308187, 86252640920, 365396207993, 1547906421765, 6557202405546, 27777188626555, 117667194149091, 498449204352288

Offset: 0

Author

Peter M. Chema, Apr 21 2016

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-12,1,1).

Crossrefs

Cf. A000045, A001906, A014445, A098317.

Programs

Maple

a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>,
         <1|1|-12|7>>^n. <<0, 1, 5, 26>>)[1, 1]:
seq(a(n), n=0..30);  # Alois P. Heinz, Apr 21 2016

Mathematica

Table[Fibonacci[3n] - Fibonacci[2n], {n, 0, 25}] (* Robert Price, Apr 21 2016 *)

PARI

a(n) = fibonacci(3*n) - fibonacci(2*n); \\ Michel Marcus, Apr 21 2016

Formula

a(n) = A014445(n) - A001906(n).

G.f.: -x*(3*x^2-2*x+1)/((x^2-3*x+1)*(x^2+4*x-1)). - Alois P. Heinz, Apr 21 2016

E.g.f.: (exp(-(sqrt(5)-2)*x)*(exp(2*sqrt(5)*x) + exp((sqrt(5)-1)*x/2) - exp((3*sqrt(5)-1)x/2) - 1))/sqrt(5). - Ilya Gutkovskiy, Apr 22 2016