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A098554 G.f.: x*(1-x^2)/((1+x^2)*(1+x+x^2). 3
0, 1, -1, -2, 3, 1, -4, 1, 3, -2, -1, 1, 0, 1, -1, -2, 3, 1, -4, 1, 3, -2, -1, 1, 0, 1, -1, -2, 3, 1, -4, 1, 3, -2, -1, 1, 0, 1, -1, -2, 3, 1, -4, 1, 3, -2, -1, 1, 0, 1, -1, -2, 3, 1, -4, 1, 3, -2, -1, 1, 0, 1, -1, -2, 3, 1, -4, 1, 3, -2, -1, 1, 0, 1, -1, -2, 3, 1, -4, 1, 3, -2, -1, 1, 0, 1, -1, -2, 3, 1, -4, 1, 3, -2, -1, 1, 0, 1, -1, -2, 3, 1, -4, 1, 3, -2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

REFERENCES

G. I. Lehrer and G. B. Segal, Homology stability for classical regular semisimple varieties, Math. Zeit., 236 (2001), 251-290; see Th. 7.12.

LINKS

Table of n, a(n) for n=0..105.

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

FORMULA

Let b(n)=sum{k=0..floor(n/2), binomial(n-k, k)(0^(n-2k)-(-1)^(n-2k)}. Then a(n)=b(n)-b(n-2), or a(n)=sum{j=0..n, b(n-j)(binomial(1, j/2)(-1)^(j/2)(1+(-1)^j)/2}. The g.f. is obtained from the g.f. x/(1+x) of 0^n-(-1)^n by applying the transformation G(x)->((1-x^2)/(1+x^2))G(x/(1+x^2)). - Paul Barry, Oct 26 2004

a(n) = (-1)^n*(A112553(n-1) - A112553(n-3)). - R. J. Mathar, Sep 27 2014

a(0)=0, a(1)=1, a(2)=-1, a(3)=-2, a(n)=a(n-1)-2*a(n-2)-a(n-3)-a(n-4). - Harvey P. Dale, Jan 16 2016

MATHEMATICA

CoefficientList[Series[x (1-x^2)/((1+x^2)(1+x+x^2)), {x, 0, 110}], x] (* or *) LinearRecurrence[{-1, -2, -1, -1}, {0, 1, -1, -2}, 110] (* Harvey P. Dale, Jan 16 2016 *)

CROSSREFS

Sequence in context: A035612 A199539 A089555 * A226081 A109201 A002946

Adjacent sequences:  A098551 A098552 A098553 * A098555 A098556 A098557

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Oct 26 2004

STATUS

approved

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Last modified March 30 04:42 EDT 2017. Contains 284296 sequences.