A052970 Expansion of (1-2*x)/(1-2*x-2*x^2+2*x^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, 313046493184, 776729176064

Offset

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1042

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

Formula

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))

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);

Mathematica

LinearRecurrence[{2, 2, -2}, {1, 0, 2}, 35] (* Paolo Xausa, Jun 04 2026 *)

Crossrefs

Sequence in context: A276054 A192305 A228797 * A220589 A109190 A016120

Adjacent sequences: A052967 A052968 A052969 * A052971 A052972 A052973

Keyword

easy,nonn,changed

Author

INRIA Encyclopedia of Combinatorial Structures, Jan 25 2000

Extensions

More terms from James Sellers, Jun 05 2000

More terms from Paolo Xausa, Jun 04 2026

Status

approved