A052970 Expansion of (1-2x)/(1-2x-2x^2+2x^3).

1, 0, 2, 2, 8, 16, 44, 104, 264, 648, 1616, 4000, 9936, 24640, 61152, 151712, 376448, 934016, 2317504, 5750144, 14267264, 35399808, 87833856, 217932800, 540733696, 1341665280, 3328932352, 8259727872, 20493989888, 50849570816, 126167665664

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1042
• Index entries for linear recurrences with constant coefficients, signature (2,2,-2).

Programs

Maple

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

Formula

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

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

Sum(-1/37*(3-15*_alpha+2*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(2*_Z^3-2*_Z^2-2*_Z+1))

Extensions

More terms from James Sellers, Jun 05 2000