login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 entries for 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 4 09:05 EST 2016. Contains 278749 sequences.