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%I #12 Jun 10 2018 20:52:10
%S 1,1,5,15,47,149,469,1479,4663,14701,46349,146127,460703,1452485,
%T 4579333,14437527,45518023,143507293,452443709,1426445343,4497236399,
%U 14178696245,44701992373,140934546279,444332462167,1400872547917,4416611574893,13924505717871
%N Expansion of (1-x)/(1-2*x-3*x^2-2*x^3).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,2).
%F a(n) = sum(k=1..n, sum(i=k..n,(sum(j=0..k, binomial(j,-3*k+2*j+i)* 3^(-3*k+2*j+i)*2^(k-j)*binomial(k,j)))*binomial(n+k-i-1,k-1))), n>0, a(0)=1. - _Vladimir Kruchinin_, May 05 2011
%t CoefficientList[Series[(1-x)/(1-2*x-3*x^2-2*x^3),{x,0,30}],x] (* or *) LinearRecurrence[{2,3,2},{1,1,5},30] (* _Harvey P. Dale_, Oct 11 2017 *)
%o (Maxima)
%o a(n):=sum(sum((sum(binomial(j,-3*k+2*j+i)*3^(-3*k+2*j+i)*2^(k-j)*binomial(k,j),j,0,k))*binomial(n+k-i-1,k-1),i,k,n),k,1,n); /* _Vladimir Kruchinin_, May 05 2011 */
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Nov 17 2002