A052962 Expansion of (1-2x^2)/(1-x-3x^2+2x^4).

1, 1, 2, 5, 9, 22, 45, 101, 218, 477, 1041, 2270, 4957, 10813, 23602, 51501, 112393, 245270, 535245, 1168053, 2549002, 5562621, 12139137, 26490894, 57810301, 126157741, 275310370, 600801805, 1311112313, 2861202246, 6243918445

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1033

Index entries for linear recurrences with constant coefficients, signature (1,3,0,-2).

Formula

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

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

Sum(-1/397*(-190*_alpha-78*_alpha^2+116*_alpha^3+15)*_alpha^(-1-n), _alpha=RootOf(1-3*_Z^2+2*_Z^4-_Z))

Maple

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

Mathematica

CoefficientList[Series[(1-2x^2)/(1-x-3x^2+2x^4), {x, 0, 30}], x] (* or *) LinearRecurrence[{1, 3, 0, -2}, {1, 1, 2, 5}, 40] (* Harvey P. Dale, Feb 20 2016 *)

Crossrefs

Sequence in context: A024822 A218966 A029726 * A173565 A268651 A342556

Adjacent sequences: A052959 A052960 A052961 * A052963 A052964 A052965

Keyword

easy,nonn

Author

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

Extensions

More terms from James A. Sellers, May 04 2000

Status

approved