This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A112690 Expansion of 1/(1+x^2-x^3-x^5). 1
 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Partial sums are A112689. LINKS Index entries for linear recurrences with constant coefficients, signature (0,-1,1,0,1) FORMULA G.f.: 1/((1+x^2)(1-x^3)). a(n) = sum{k=0..n, sum{j=0..floor((k+1)/2)), (-1)^(k-j)*C(k-j+1, j-1)}}. a(n+12) = a(n) = 1/6 + A057077(n+1)/2 + A061347(n+1)/3. [R. J. Mathar, Feb 23 2009] a(n+10) = (A000100(n)(mod 2))*(-1)^(1+[n/2]). - John M. Campbell, Jul 07 2016 From Ilya Gutkovskiy, Jul 07 2016: (Start) E.g.f.: (3*sin(x) + 3*cos(x) + exp(x) - 4*exp(-x/2)*cos(sqrt(3)*x/2))/6. a(n) = (3*sin(Pi*n/2) + 3*cos(Pi*n/2) - 4*cos(2*Pi*n/3) + 1)/6. (End) MATHEMATICA LinearRecurrence[{0, -1, 1, 0, 1}, {0, 1, 0, -1, 1}, 100] (* Vincenzo Librandi, Jul 07 2016 *) PROG (PARI) concat(0, Vec(1/(1+x^2-x^3-x^5) + O(x^80))) \\ Michel Marcus, Jul 07 2016 (PARI) a(n) = round(real((exp(-2/3*I*n*Pi)*(-4+(3+3*I)*exp((I*n*Pi)/6) + 2*exp((2*I*n*Pi)/3) + (3-3*I)*exp((7*I*n*Pi)/6) - 4*exp((4*I*n*Pi)/3)))/12)) \\ Colin Barker, Jul 07 2016 CROSSREFS Cf. A000100, A057077, A061347, A112689. Sequence in context: A284893 A316829 A277674 * A316343 A288864 A115971 Adjacent sequences:  A112687 A112688 A112689 * A112691 A112692 A112693 KEYWORD easy,sign AUTHOR Paul Barry, Sep 15 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 19 17:45 EST 2019. Contains 319309 sequences. (Running on oeis4.)