A052977 - OEIS

%I #25 Jun 05 2021 16:38:53

%S 1,1,1,3,5,8,15,27,47,84,150,266,473,842,1497,2662,4735,8421,14976,

%T 26635,47370,84246,149830,266470,473911,842841,1498976,2665898,

%U 4741245,8432208,14996510,26670987,47433807,84360059,150032645,266830001

%N Expansion of (1-x)(1+x)/(1 - x - x^2 - x^3 + x^5).

%C Equals INVERT transform of (1, 0, 2, 0, 1, 0, 1, ...). - _Gary W. Adamson_, Apr 28 2009

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1049">Encyclopedia of Combinatorial Structures 1049</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,0,-1).

%F G.f.: -(-1+x^2)/(1 - x - x^2 - x^3 + x^5).

%F Recurrence: {a(1)=1, a(0)=1, a(2)=1, a(3)=3, a(4)=5, a(n) - a(n+2) - a(n+3) - a(n+4) + a(n+5) = 0}.

%F a(n) = Sum(-1/7031*(-798-714*_alpha^2-1887*_alpha+410*_alpha^4+986*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-_Z^3-_Z-_Z^2+_Z^5)). [in Maple notation]

%p spec := [S,{S=Sequence(Prod(Union(Sequence(Prod(Z,Z)),Prod(Z,Z)),Z))},unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);

%t CoefficientList[Series[(1-x)(1+x)/(1-x-x^2-x^3+x^5),{x,0,40}],x] (* or *) LinearRecurrence[{1,1,1,0,-1},{1,1,1,3,5},40] (* _Harvey P. Dale_, Apr 26 2018 *)

%K easy,nonn

%O 0,4

%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000

%E More terms from _James A. Sellers_, Jun 06 2000