A052979 Expansion of (1-x)(1+x)/(1-2*x-3*x^2+2*x^4).

1, 2, 6, 18, 52, 154, 452, 1330, 3912, 11506, 33844, 99546, 292800, 861226, 2533164, 7450914, 21915720, 64461730, 189604292, 557691946, 1640365328, 4824883034, 14191653468, 41742572146, 122779374040, 361136698450, 1062228212084

Offset

0,2

Links

Table of n, a(n) for n=0..26.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1051

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

Formula

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

Recurrence: {a(0)=1, a(1)=2, a(2)=6, a(3)=18, 2*a(n)-3*a(n+2)-2*a(n+3)+a(n+4)=0}

Sum(-1/22*(-3-7*_alpha+4*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-3*_Z^2+2*_Z^4-2*_Z))

Maple

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

Mathematica

CoefficientList[Series[(1-x)(1+x)/(1-2x-3x^2+2x^4), {x, 0, 30}], x] (* or *) LinearRecurrence[{2, 3, 0, -2}, {1, 2, 6, 18}, 30] (* Harvey P. Dale, Oct 18 2019 *)

Crossrefs

Sequence in context: A077935 A077835 A077984 * A005507 A252822 A094864

Adjacent sequences: A052976 A052977 A052978 * A052980 A052981 A052982

Keyword

easy,nonn

Author

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

Extensions

More terms from James A. Sellers, Jun 06 2000

Status

approved