A052974 Expansion of (1 - 2x)/(1 - 2x - x^2 - x^3 + 2x^4).

1, 0, 1, 3, 5, 14, 34, 81, 200, 487, 1187, 2899, 7072, 17256, 42109, 102748, 250717, 611779, 1492805, 3642610, 8888370, 21688597, 52922564, 129136875, 315108171, 768898587, 1876197092, 4578127192, 11171133721, 27258794552, 66514455833

Offset

0,4

Links

Table of n, a(n) for n=0..30.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1046

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

Formula

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

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

Sum(1/4999*(-159+1343*_alpha-450*_alpha^2+136*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z-_Z^3+2*_Z^4-_Z^2))

Maple

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

Mathematica

CoefficientList[Series[(1 - 2 x)/(1 - 2 x - x^2 - x^3 + 2 x^4), {x, 0, 40}], x] (* Wesley Ivan Hurt, Jan 15 2017 *)

Crossrefs

Sequence in context: A222380 A271867 A295064 * A284415 A318227 A363542

Adjacent sequences: A052971 A052972 A052973 * A052975 A052976 A052977

Keyword

easy,nonn

Author

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

Extensions

More terms from James A. Sellers, Jun 06 2000

Status

approved