%I #17 Jun 17 2020 07:33:29

%S 1,2,6,18,55,169,520,1601,4930,15182,46754,143983,443409,1365520,

%T 4205249,12950466,39882198,122821042,378239143,1164823609,3587185688,

%U 11047081345,34020543362,104769516446,322647744322,993624581343,3059961912097,9423445312544

%N Expansion of (1-x-x^2)/((x-1)*(x^3+3*x^2+2*x-1)).

%C Row sums of the triangle in A152440.

%H Vincenzo Librandi, <a href="/A238236/b238236.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-2,-1).

%F G.f.: (1-x-x^2)/(1-3*x-x^2+2*x^3+x^4).

%F a(n) = 3*a(n-1) + a(n-2) -2*a(n-3) - a(n-4), a(0) = 1, a(1) = 2, a(2) = 6, a(3) = 18.

%F a(n) = A097472(n) - A097472(n-1) - A097472(n-2).

%F a(n) = A060945(2*n).

%F a(n)-a(n-1) = A099098(n). - _R. J. Mathar_, Jun 17 2020

%t CoefficientList[Series[(1 - x - x^2)/(1 - 3 x - x^2 + 2 x^3 + x^4), {x, 0, 40}], x ](* _Vincenzo Librandi_, Feb 22 2014 *)

%Y Cf. A097472, A152440, A099098 (first differences).

%K nonn,easy

%O 0,2

%A _Philippe Deléham_, Feb 20 2014