A171160 - OEIS

%I #63 Jul 07 2022 16:20:06

%S 3,4,10,18,38,74,150,298,598,1194,2390,4778,9558,19114,38230,76458,

%T 152918,305834,611670,1223338,2446678,4893354,9786710,19573418,

%U 39146838,78293674,156587350,313174698,626349398,1252698794,2505397590,5010795178,10021590358

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

%H J. Mulder, <a href="/A171160/b171160.txt">Table of n, a(n) for n = 0..2999</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2).

%F a(n) = (1/3)*(2*(-1)^n + 7*2^n), with n>=0. - _Paolo P. Lava_, Dec 14 2009

%F G.f.: -(x+3) / ((x+1)*(2*x-1)). - _Colin Barker_, Feb 10 2015

%F From _Paul Curtz_, Jun 03 2022: (Start)

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

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

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

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

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

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

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

%F a(n) = 2*A062092(n-1), for n>0; 2*a(n) = A083595(n+1). - _Paul Curtz_, Jun 08 2022

%t f[n_]:=2/(n+1);x=5;Table[x=f[x];Numerator[x],{n,0,5!}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 12 2010 *)

%t LinearRecurrence[{1,2},{3,4},40] (* _Harvey P. Dale_, Sep 04 2013 *)

%o (PARI) Vec(-(x+3)/((x+1)*(2*x-1)) + O(x^100)) \\ _Colin Barker_, Feb 10 2015

%Y Cf. A001045, A078008, A175805.

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

%Y Cf. A092297, A154879.

%Y Cf. A062092, A083595.

%K nonn,easy

%O 0,1

%A _Paul Curtz_, Dec 04 2009

%E Edited by _N. J. A. Sloane_, Dec 05 2009

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

%E More terms from _Max Alekseyev_, Apr 24 2010