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

Author

Paul Curtz, Dec 05 2009

Keywords

• nonn
• easy

Comments

From 14, the last 2 digits are of period 4: repeat [14, 27, 54, 07]. - Paul Curtz, Nov 22 2024

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Crossrefs

Cf. A000035, A000975, A048573, A136412 (1st bisection), 2*A136412 (2nd bisection).

Cf. A010712, A160113.

Programs

Magma

[( 10*2^n+3-(-1)^n )/6: n in [0..40]]; // Vincenzo Librandi, Aug 05 2011

Mathematica

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

PARI

a(n)=(10<Charles R Greathouse IV, Jul 07 2011

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

Extensions

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