OFFSET
0,4
COMMENTS
Equals INVERT transform of (1, 0, 2, 0, 1, 0, 1, ...). - Gary W. Adamson, Apr 28 2009
LINKS
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
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from James A. Sellers, Jun 06 2000
STATUS
approved