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Expansion of (1-x)^(-1)/(1-x-2*x^2-x^3).
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%I #27 Sep 29 2015 07:18:30

%S 1,2,5,11,24,52,112,241,518,1113,2391,5136,11032,23696,50897,109322,

%T 234813,504355,1083304,2326828,4997792,10734753,23057166,49524465,

%U 106373551,228479648,490751216,1054084064,2264066145,4862985490,10445201845,22435238971,48188628152

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

%C Diagonal sums of triangle using cumulative sums of odd-indexed rows of Pascal's triangle (cf. A020988). - _Paul Barry_, May 18 2003

%H Alois P. Heinz, <a href="/A077864/b077864.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(0)=1, a(1)=2, a(2)=5, a(3)=11, a(n)=2*a(n-1)+a(n-2)-a(n-3)-a(n-4) for n>3. - _Philippe Deléham_, Oct 25 2006

%F a(n) = term (4,1) in the 4x4 matrix [1,1,0,0; 2,0,1,0; 1,0,0,0; 1,0,0,1]^(n+1). - _Alois P. Heinz_, Jul 24 2008

%F Conjecture: a(n) = Sum_{j=0..n/2} A027907(n+1-j,2*j+1), n >= 0. - _Werner Schulte_, Sep 29 2015

%p a := n -> (Matrix([[1,1,0,0], [2,0,1,0], [1,0,0,0], [1,0,0,1]])^(n+1))[4,1]; seq(a(n), n=0..50); # _Alois P. Heinz_, Jul 24 2008

%t CoefficientList[Series[(1-x)^(-1)/(1-x-2x^2-x^3),{x,0,40}],x] (* or *) LinearRecurrence[{2,1,-1,-1},{1,2,5,11},40] (* _Harvey P. Dale_, Oct 08 2014 *)

%o (PARI) Vec((1-x)^(-1)/(1-x-2*x^2-x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 17 2002