A052977 Expansion of (1-x)(1+x)/(1 - x - x^2 - x^3 + x^5).

1, 1, 1, 3, 5, 8, 15, 27, 47, 84, 150, 266, 473, 842, 1497, 2662, 4735, 8421, 14976, 26635, 47370, 84246, 149830, 266470, 473911, 842841, 1498976, 2665898, 4741245, 8432208, 14996510, 26670987, 47433807, 84360059, 150032645, 266830001

Offset

0,4

Comments

Equals INVERT transform of (1, 0, 2, 0, 1, 0, 1, ...). - Gary W. Adamson, Apr 28 2009

Links

Table of n, a(n) for n=0..35.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1049

Index entries for linear recurrences with constant coefficients, signature (1,1,1,0,-1).

Formula

G.f.: -(-1+x^2)/(1 - x - x^2 - x^3 + x^5).

Recurrence: {a(1)=1, a(0)=1, a(2)=1, a(3)=3, a(4)=5, a(n) - a(n+2) - a(n+3) - a(n+4) + a(n+5) = 0}.

a(n) = Sum(-1/7031*(-798-714*_alpha^2-1887*_alpha+410*_alpha^4+986*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-_Z^3-_Z-_Z^2+_Z^5)). [in Maple notation]

Maple

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

Mathematica

CoefficientList[Series[(1-x)(1+x)/(1-x-x^2-x^3+x^5), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 1, 1, 0, -1}, {1, 1, 1, 3, 5}, 40] (* Harvey P. Dale, Apr 26 2018 *)

Crossrefs

Sequence in context: A290630 A359851 A193147 * A191633 A215327 A208723

Adjacent sequences: A052974 A052975 A052976 * A052978 A052979 A052980

Keyword

easy,nonn

Author

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

Extensions

More terms from James A. Sellers, Jun 06 2000

Status

approved