A168648 a(n) = (10*2^n + 2*(-1)^n)/3 for n > 0; a(0) = 1.

1, 6, 14, 26, 54, 106, 214, 426, 854, 1706, 3414, 6826, 13654, 27306, 54614, 109226, 218454, 436906, 873814, 1747626, 3495254, 6990506, 13981014, 27962026, 55924054, 111848106, 223696214, 447392426, 894784854, 1789569706, 3579139414

Offset: 0

Author

Klaus Brockhaus, Dec 01 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (1,2).

Crossrefs

Cf. A084214 ((5*2^n -3*0^n +4*(-1)^n)/6).

Programs

Magma

[1] cat [ (10*2^n+2*(-1)^n)/3: n in [1..30] ];

Mathematica

{1}~Join~Table[(10*2^n + 2*(-1)^n)/3, {n,40}] (* or *)
{1}~Join~LinearRecurrence[{1,2}, {6,14}, 40] (* G. C. Greubel, Jul 28 2016 *)

PARI

a(n) = if(n, (10<Charles R Greathouse IV, Jul 29 2016

Sage

[1]+[(10*2^n +2*(-1)^n)/3 for n in (1..40)] # G. C. Greubel, Feb 05 2021

Formula

a(n) = A084214(n+2) for n > 0.

a(n) = a(n-1) + 2*a(n-2) for n > 2; a(0) = 1, a(1) = 6, a(2) = 14.

G.f.: (1+2*x)*(1+3*x)/((1+x)*(1-2*x)).

E.g.f.: (1/3)*(10*exp(2*x) - 9 + 2*exp(-x)). - G. C. Greubel, Jul 28 2016