The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A008818 Expansion of (1+2*x^3+x^4)/((1-x^2)^2*(1-x^4)); Molien series for 3-dimensional representation of group 2x = [ 2+,4+ ] = CC_4 = C4. 4
 1, 0, 2, 2, 5, 4, 8, 8, 13, 12, 18, 18, 25, 24, 32, 32, 41, 40, 50, 50, 61, 60, 72, 72, 85, 84, 98, 98, 113, 112, 128, 128, 145, 144, 162, 162, 181, 180, 200, 200, 221, 220, 242, 242, 265, 264, 288, 288, 313, 312, 338, 338, 365, 364, 392, 392, 421, 420, 450 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES B. Sturmfels, Algorithms in Invariant Theory, Springer, p. 42. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,-1,1). FORMULA G.f.: (1 -x +x^2 -x^3)/( (1+x^2)*(1+x)^2*(1-x)^3 ). - R. J. Mathar, Dec 18 2014 a(n) = (5 + 7*(-1)^n + (2-i*2)*(-i)^n + (2+2*i)*i^n + 2*(3+(-1)^n)*n + 2*n^2) / 16 where i = sqrt(-1). - Colin Barker, Oct 15 2015 a(n) = (n/2 + 9/4)*floor(n/2) + floor((n+1)/4) - (n^2 + 7*n)/8 + 1. - Ridouane Oudra, Oct 17 2020 MAPLE (1+2*x^3+x^4)/((1-x^2)^2*(1-x^4)): seq(coeff(series(%, x, n+1), x, n), n=0..60); MATHEMATICA CoefficientList[Series[(1+2x^3+x^4)/((1-x^2)^2(1-x^4)), {x, 0, 60}], x] (* Vincenzo Librandi, Aug 15 2013 *) LinearRecurrence[{1, 1, -1, 1, -1, -1, 1}, {1, 0, 2, 2, 5, 4, 8}, 60] (* Harvey P. Dale, Aug 20 2017 *) PROG (PARI) a(n) = (5 + 7*(-1)^n + (2-I*2)*(-I)^n + (2+2*I)*I^n + 2*(3+(-1)^n)*n + 2*n^2) / 16 \\ Colin Barker, Oct 15 2015 (Magma) R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+2*x^3+x^4)/((1-x^2)^2*(1-x^4)) )); // G. C. Greubel, Sep 12 2019 (Sage) def A008818_list(prec): P. = PowerSeriesRing(ZZ, prec) return P((1+2*x^3+x^4)/((1-x^2)^2*(1-x^4))).list() A008818_list(60) # G. C. Greubel, Sep 12 2019 (GAP) a:=[1, 0, 2, 2, 5, 4, 8];; for n in [8..60] do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-4]-a[n-5]-a[n-6]+a[n-7]; od; a; # G. C. Greubel, Sep 12 2019 CROSSREFS Expansions of the form (1 +2*x^(2*m+1) +x^(4*m))/((1-x^2)^2*(1-x^(4*m))): this sequence (m=1), A008819 (m=2), A008820 (m=3), A008821 (m=4). Sequence in context: A007281 A101085 A088880 * A089599 A206556 A127683 Adjacent sequences: A008815 A008816 A008817 * A008819 A008820 A008821 KEYWORD nonn,easy AUTHOR STATUS approved

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

Last modified November 28 05:56 EST 2022. Contains 358407 sequences. (Running on oeis4.)