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A105385 Expansion of (1-x^2)/(1-x^5). 1
1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Binomial transform is A103311(n+1). Consecutive pair sums of A105384. Periodic {1,0,-1,0,0}.

LINKS

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

Index to sequences with linear recurrences with constant coefficients, signature (-1,-1,-1,-1).

FORMULA

G.f.: (1+x)/(1+x+x^2+x^3+x^4); a(n)=sqrt(1/5-2sqrt(5)/25)cos(4*pi*n/5+pi/10)+sqrt(5)sin(4*pi*n/5+pi/10)/5+ sqrt(2sqrt(5)/25+1/5)cos(2*pi*n/5+3*pi/10)+sqrt(5)sin(2*pi*n/5+3*pi/10)/5

a(n)=-(1/5)*{[n mod 5]+[(n+2) mod 5]-[(n+3) mod 5]-[(n+4) mod 5]}, with n>=0. - Paolo P. Lava, Jun 01 2007

a(n)=A092202(n+1). [From R. J. Mathar, Aug 28 2008]

a(0)=1, a(1)=0, a(2)=-1, a(3)=0, a(n)=a(n-1)-a(n-2)-a(n-3)-a(n-4). - Harvey P. Dale, Mar 10 2013

MATHEMATICA

CoefficientList[Series[(1-x^2)/(1-x^5), {x, 0, 100}], x] (* or *) PadRight[{}, 100, {1, 0, -1, 0, 0}] (* or *) LinearRecurrence[{-1, -1, -1, -1}, {1, 0, -1, 0}, 100] (* Harvey P. Dale, Mar 10 2013 *)

CROSSREFS

Cf. A198517 (unsigned version).

Sequence in context: A127829 A127831 A164364 * A090626 A129569 A030658

Adjacent sequences:  A105382 A105383 A105384 * A105386 A105387 A105388

KEYWORD

sign,easy

AUTHOR

Paul Barry, Apr 02 2005

STATUS

approved

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Last modified December 21 08:32 EST 2014. Contains 252299 sequences.