A083694 a(n) = 2*A002532(n).

0, 2, 4, 18, 56, 202, 684, 2378, 8176, 28242, 97364, 335938, 1158696, 3997082, 13787644, 47560698, 164059616, 565922722, 1952143524, 6733900658, 23228518936, 80126541162, 276395677004, 953424059818, 3288826504656

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (2,5).

Formula

G.f.: 2*x / (1 - 2*x - 5*x^2).

a(n) = 2*a(n-1) + 5*a(n-2), a(0)=0, a(1)=2.

a(n) = 1 / sqrt(6) * ( (1+sqrt(6))^n - (1-sqrt(6))^n ).

a(n) = 2 * A002533(n-1) + a(n-1).

Mathematica

CoefficientList[Series[2x/(1-2x-5x^2), {x, 0, 25}], x]
LinearRecurrence[{2, 5}, {0, 2}, 40]  (* Harvey P. Dale, Nov 03 2011 *)
With[{c=Sqrt[6]}, Simplify/@ Table[((1-c)^n+c (1-c)^n-(1+c)^n+c (1+c)^n)/(5c), {n, 30}]] (* Harvey P. Dale, Nov 03 2011 *)

Crossrefs

Sequence in context: A093045 A330432 A317887 * A179040 A241685 A009679

Adjacent sequences: A083691 A083692 A083693 * A083695 A083696 A083697

Keyword

easy,nonn

Author

Mario Catalani (mario.catalani(AT)unito.it), May 03 2003

Status

approved