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A084100 Expansion of (1+x-x^2-x^3)/(1+x^2). 4
1, 1, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums are A084099.

The unsigned sequence 1,1,2,2,2,2,.. has g.f. (1+x^2)/(1-x) and a(n)=sum{k=0..n, binomial(1,k/2)(1+(-1)^k)/2}. Its partial sums are A004275(n+1). The sequence 1,-1,2,-2,2,-2,... has g.f. (1+x^2)/(1+x) and a(n)=sum{k=0..n, (-1)^(n-k)binomial(1,k/2)(1+(-1)^k)/2}. - Paul Barry, Oct 15 2004

LINKS

Table of n, a(n) for n=0..90.

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

FORMULA

Euler transform of length 4 sequence [1, -3, 0, 1]. - Michael Somos, Jan 05 2017

G.f.: (1 + x) * (1 - x^2) / (1 + x^2). - Michael Somos, Jan 05 2017

a(n) = a(1-n) for all n in Z. - Michael Somos, Jan 05 2017

a(2*n) = a(2*n + 1) = A280560(n) for all n in Z. - Michael Somos, Jan 05 2017

EXAMPLE

G.f. = 1 + x - 2*x^2 - 2*x^3 + 2*x^4 + 2*x^5 - 2*x^6 - 2*x^7 + 2*x^8 + 2*x^9 + ...

MATHEMATICA

CoefficientList[Series[(1+x-x^2-x^3)/(1+x^2), {x, 0, 100}], x]  (* Harvey P. Dale, Apr 20 2011 *)

a[ n_] := (-1)^Quotient[n, 2] If[ Quotient[n, 2] != 0, 2, 1]; (* Michael Somos, Jan 05 2017 *)

PROG

(PARI) {a(n) = (-1)^(n\2) * if( n\2, 2, 1)}; /* Michael Somos, Jan 05 2017 */

CROSSREFS

Cf. A084099, A280560.

Sequence in context: A077433 A211665 A065685 * A130130 A046698 A007395

Adjacent sequences:  A084097 A084098 A084099 * A084101 A084102 A084103

KEYWORD

easy,sign

AUTHOR

Paul Barry, May 15 2003

STATUS

approved

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Last modified March 18 13:47 EDT 2019. Contains 321289 sequences. (Running on oeis4.)