A127261 a(0)=2, a(1)=2, a(n) = 2*a(n-1) + 10*a(n-2).

2, 2, 24, 68, 376, 1432, 6624, 27568, 121376, 518432, 2250624, 9685568, 41877376, 180610432, 779994624, 3366093568, 14532133376, 62725202432, 270771738624, 1168795501568, 5045308389376

Offset

0,1

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (2, 10).

Formula

a(n) = (1+sqrt(11))^n + (1-sqrt(11))^n, with n >= 0. - Paolo P. Lava, Jul 31 2008

G.f.: G(0), where G(k)= 1 + 1/(1 - x*(11*k-1)/(x*(11*k+10) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 18 2013

G.f.: (2(x-1))/(2*x(5*x+1)-1). - Harvey P. Dale, Oct 15 2013

Maple

a[0]:=2:a[1]:=2:for i from 2 to 40 do a[i]:=2*a[i-1]+10*a[i-2] od: seq(a[n], n=0..40);

Mathematica

LinearRecurrence[{2, 10}, {2, 2}, 30] (* or *) CoefficientList[Series[(2*(x-1))/(2*x(5*x+1)-1), {x, 0, 30}], x] (* Harvey P. Dale, Oct 15 2013 *)

Prog

(Sage) [lucas_number2(n, 2, -10) for n in range(0, 21)] # Zerinvary Lajos, Apr 30 2009

Crossrefs

Sequence in context: A156447 A272641 A334123 * A239531 A194130 A356908

Adjacent sequences: A127258 A127259 A127260 * A127262 A127263 A127264

Keyword

easy,nonn

Author

Miklos Kristof, Mar 27 2007

Status

approved