OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2, -1, 1, -2, 1).
FORMULA
a(n) = (3*(n-1)*(n-4) + 94 - 2*cos(2*n*Pi/3) - 2*sqrt(3)*sin(2*n*Pi/3) + 4*(-1)^n*cos(n*Pi/3))/18 for n >=6. - G. C. Greubel, Aug 04 2019
MATHEMATICA
CoefficientList[Series[(1+x^11)/(1-x)/(1-x^2)/(1-x^3), {x, 0, 60}], x] (* Harvey P. Dale, Aug 12 2014 *)
Join[{1, 1, 2, 3, 4, 5}, Table[(3*(n-1)*(n-4) +94 -2*Cos[2*n*Pi/3] -
2*Sqrt[3]*Sin[2*n*Pi/3] +4*(-1)^n*Cos[n*Pi/3])/18, {n, 6, 60}]] (* G. C. Greubel, Aug 04 2019 *)
PROG
(PARI) my(x='x+O('x^60)); Vec((1+x^11)/((1-x)*(1-x^2)*(1-x^3))) \\ G. C. Greubel, Aug 04 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^11)/((1-x)*(1-x^2)*(1-x^3)) )); // G. C. Greubel, Aug 04 2019
(Sage) ((1+x^11)/((1-x)*(1-x^2)*(1-x^3))).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Aug 04 2019
(GAP) a:=[7, 8, 10, 12, 14];; for n in [6..60] do a[n]:=2*a[n-1]-a[n-2]+ a[n-3]-2*a[n-4]+a[n-5]; od; Concatenation([1, 1, 2, 3, 4, 5], a); # G. C. Greubel, Aug 04 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved