OFFSET
0,8
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,5,-5,-10,10,10,-10,-5,5,1,-1).
FORMULA
a(n) = a(n-1) + 5*a(n-2) - 5*a(n-3) - 10*a(n-4) + 10*a(n-5) + 10*a(n-6) - 10*a(n-7) - 5*a(n-8) + 5*a(n-9) + a(n-10) - a(n-11), with a(0)=0, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=1, a(7)=3, a(8)=12, a(9)=24, a(10)=60. - Harvey P. Dale, Jun 26 2012
G.f.: x^6*(1+2*x+4*x^2+2*x^3+x^4)/((1-x)^6*(1+x)^5). - Colin Barker, Mar 01 2015
From R. J. Mathar, Sep 23 2021: (Start)
a(2*n+1) = A004282(n-2).
a(2*n) = A004302(n-2).
From G. C. Greubel, Apr 08 2022: (Start)
a(n) = (1/768)*((-1)^n*(45 -65*n +38*n^2 -10*n^3 +n^4) -45 +193*n -230*n^2 +114*n^3 -25*n^4 +2*n^5).
E.g.f.: (1/768)*((45 +36*x +15*x^2 +4*x^3 +x^4)*exp(-x) + (-45 +54*x -33*x^2 + 14*x^3 -5*x^4 +2*x^5)*exp(x)). (End)
MATHEMATICA
Table[(Times@@Floor/@(n/2-Range[0, 4]/2))/12, {n, 0, 50}] (* or *) LinearRecurrence[ {1, 5, -5, -10, 10, 10, -10, -5, 5, 1, -1}, {0, 0, 0, 0, 0, 0, 1, 3, 12, 24, 60}, 50] (* Harvey P. Dale, Jun 26 2012 *)
PROG
(PARI) concat([0, 0, 0, 0, 0, 0], Vec(x^6*(x^4+2*x^3+4*x^2+2*x+1)/((x-1)^6*(x+1)^5) + O(x^100))) \\ Colin Barker, Mar 01 2015
(Magma) [(&*[Floor((n-j)/2):j in [0..4]])/12: n in [0..60]]; // G. C. Greubel, Apr 08 2022
(SageMath) [(1/768)*((-1)^n*(45 -65*n +38*n^2 -10*n^3 +n^4) -45 +193*n -230*n^2 +114*n^3 -25*n^4 +2*n^5) for n in (0..60)] # G. C. Greubel, Apr 08 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved