%I #10 Aug 20 2015 14:00:28

%S 1,0,1,2,3,8,13,30,55,116,225,458,907,1824,3637,7286,14559,29132,

%T 58249,116514,233011,466040,932061,1864142,3728263,7456548,14913073,

%U 29826170,59652315,119304656,238609285,477218598,954437167,1908874364,3817748697

%N Expansion of (1-2x^2)/((1-2x)(1+x)^2).

%C Inverse binomial transform of phi(phi(3^n)).

%H Harvey P. Dale, <a href="/A113954/b113954.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,2).

%F a(n)=3a(n-2)+2a(n-3); a(n)=2^(n+1)/9+(7-3n)(-1)^n/9; a(n)=a(n)=sum{k=0..n, (-1)^(n-k)*C(n, k)phi(phi(3^k))}; a(n)=sum{k=0..n, (-1)^(n-k)*C(n, k)(2*3^k/9+C(1, k)/3+4*C(0, k)/9)}; a(n)=sum{k=0..n, J(n-k+1)((-1)^(k+1)-2C(1, k)+4C(0, k))} where J(n)=A001045(n).

%t CoefficientList[Series[(1-2x^2)/((1-2x)(1+x)^2),{x,0,40}],x] (* or *) LinearRecurrence[{0,3,2},{1,0,1},40] (* _Harvey P. Dale_, Aug 20 2015 *)

%Y Cf. A103196.

%K easy,nonn

%O 0,4

%A _Paul Barry_, Nov 09 2005