A171160 a(n) = a(n-1) + 2*a(n-2) with a(0)=3, a(1)=4.

3, 4, 10, 18, 38, 74, 150, 298, 598, 1194, 2390, 4778, 9558, 19114, 38230, 76458, 152918, 305834, 611670, 1223338, 2446678, 4893354, 9786710, 19573418, 39146838, 78293674, 156587350, 313174698, 626349398, 1252698794, 2505397590, 5010795178, 10021590358

Offset: 0

Author

Paul Curtz, Dec 04 2009

Keywords

• nonn
• easy

Links

• J. Mulder, Table of n, a(n) for n = 0..2999
• Index entries for linear recurrences with constant coefficients, signature (1,2).

Crossrefs

Cf. A001045, A078008, A175805.

Cf. A062510, A083582, (-1)^n*A140966.

Cf. A092297, A154879.

Cf. A062092, A083595.

Programs

Mathematica

f[n_]:=2/(n+1);x=5;Table[x=f[x];Numerator[x],{n,0,5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 12 2010 *)
LinearRecurrence[{1,2},{3,4},40] (* Harvey P. Dale, Sep 04 2013 *)

PARI

Vec(-(x+3)/((x+1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Feb 10 2015

Formula

a(n) = (1/3)*(2*(-1)^n + 7*2^n), with n>=0. - Paolo P. Lava, Dec 14 2009

G.f.: -(x+3) / ((x+1)*(2*x-1)). - Colin Barker, Feb 10 2015

From Paul Curtz, Jun 03 2022: (Start)

a(n) = A078008(n) + A078008(n+1) + A078008(n+2).

a(n) = 2^(n+1) + A078008(n).

a(n) = A001045(n+3) - A001045(n).

(a(n) + a(n+1) = a(n+2) - a(n) = A005009(n).)

a(n) + a(n+3) = A175805(n).

a(n) = A062510(n) + A083582(n-1) with A083582(-1) = 3.

a(n) = A092297(n) + A154879(n). (End)

a(n) = 2*A062092(n-1), for n>0; 2*a(n) = A083595(n+1). - Paul Curtz, Jun 08 2022

Extensions

Edited by N. J. A. Sloane, Dec 05 2009

More terms from J. Mulder (jasper.mulder(AT)planet.nl), Jan 28 2010

More terms from Max Alekseyev, Apr 24 2010