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A052989 Expansion of ( 1-x ) / ( 1-x-x^2-x^4+x^5 ). 0
1, 0, 1, 1, 3, 3, 7, 10, 19, 29, 52, 84, 145, 239, 407, 678, 1146, 1918, 3232, 5421, 9121, 15314, 25749, 43252, 72701, 122146, 205282, 344931, 579662, 974038, 1636836, 2750523, 4622090, 7766989, 13051877, 21932553, 36855997, 61933449, 104074334 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
G.f.: -(-1+x)/(1-x-x^2-x^4+x^5)
Recurrence: {a(1)=0, a(0)=1, a(2)=1, a(3)=1, a(4)=3, a(n)-a(n+1)-a(n+3)-a(n+4)+a(n+5) =0}
Sum(-1/8519*(-389-2111*_alpha+619*_alpha^2-358*_alpha^3+541*_alpha^4)*_alpha^(-1-n), _alpha=RootOf(1-_Z-_Z^2-_Z^4+_Z^5))
MAPLE
spec := [S, {S=Sequence(Prod(Union(Prod(Z, Z), Sequence(Z)), Z, Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
MATHEMATICA
CoefficientList[Series[(1-x)/(1-x-x^2-x^4+x^5), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 1, 0, 1, -1}, {1, 0, 1, 1, 3}, 40] (* Harvey P. Dale, Sep 01 2017 *)
CROSSREFS
Sequence in context: A013915 A136445 A326269 * A358823 A252750 A287274
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from James A. Sellers, Jun 06 2000
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)