A171231 a(n) = (10*2^n + 3 - (-1)^n)/6.

2, 4, 7, 14, 27, 54, 107, 214, 427, 854, 1707, 3414, 6827, 13654, 27307, 54614, 109227, 218454, 436907, 873814, 1747627, 3495254, 6990507, 13981014, 27962027, 55924054, 111848107, 223696214, 447392427, 894784854, 1789569707

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Formula

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3), n >= 3.

a(n+1) - a(n) = A048573(n-1).

a(n) = 2*A000975(n+1) - 3*A000975(n-1).

a(n) - a(n-2) = 5*2^n.

a(n+1) - 2*a(n) = ((-1)^n-1)/2 = -A000035(n).

G.f.: ( 2-3*x^2 ) / ( (x-1)*(2*x-1)*(1+x) ). - R. J. Mathar, Jul 07 2011

a(n) = ceiling( (5/3)*(2^n) ). - Wesley Ivan Hurt, Jun 28 2013

Mathematica

LinearRecurrence[{2, 1, -2}, {2, 4, 7}, 40] (* Harvey P. Dale, Feb 11 2015 *)

Prog

(PARI) a(n)=(10<<n+3)\/6 \\ Charles R Greathouse IV, Jul 07 2011
(Magma) [( 10*2^n+3-(-1)^n )/6: n in [0..40]]; // Vincenzo Librandi, Aug 05 2011

Crossrefs

Sequence in context: A155099 A136322 A160113 * A094057 A119267 A144978

Adjacent sequences: A171228 A171229 A171230 * A171232 A171233 A171234

Keyword

nonn,easy

Author

Paul Curtz, Dec 05 2009

Extensions

Definition replaced by the Lava formula of 2009. Contents converted to formulas. - R. J. Mathar, Jul 07 2011

Status

approved