A052904 Expansion of (1-x)/(1-2x-4x^2+4x^3).

1, 1, 6, 12, 44, 112, 352, 976, 2912, 8320, 24384, 70400, 205056, 594176, 1726976, 5010432, 14552064, 42237952, 122642432, 356028416, 1033674752, 3000893440, 8712372224, 25293619200, 73433153536, 213191294976, 618940727296

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 882
• Index entries for linear recurrences with constant coefficients, signature (2,4,-4).

Programs

Maple

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

Mathematica

CoefficientList[Series[(1-x)/(1-2x-4x^2+4x^3),{x,0,30}],x] (* or *) LinearRecurrence[{2,4,-4},{1,1,6},30] (* Harvey P. Dale, Jan 17 2013 *)

Formula

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

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

Sum(-1/37*(-4-14*_alpha+13*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z-4*_Z^2+4*_Z^3))

Extensions

More terms from James Sellers, Jun 08 2000