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Expansion of (1-x)^2/((1-x)^3-2x^4).
2

%I #13 Apr 04 2019 04:48:58

%S 1,1,1,1,3,9,21,41,75,141,281,577,1179,2369,4709,9353,18659,37365,

%T 74889,149937,299827,599289,1198101,2396137,4793051,9587421,19175449,

%U 38349409,76695403,153388273,306778917,613566153,1227140787,2454279365

%N Expansion of (1-x)^2/((1-x)^3-2x^4).

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

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

%F a(n) = 3a(n-1)-3a(n-2)+a(n-3)+2a(n-4).

%F a(n) = Sum_{k=0..floor(n/3)} binomial(n-k,3k)*2^k.

%t CoefficientList[Series[(1-x)^2/((1-x)^3-2x^4),{x,0,50}],x] (* _Harvey P. Dale_, Feb 25 2011 *)

%K easy,nonn

%O 0,5

%A _Paul Barry_, Jul 25 2004