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A008754
Expansion of (1+x^11)/((1-x)*(1-x^2)*(1-x^3)).
1
1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 17, 20, 23, 27, 31, 35, 40, 45, 50, 56, 62, 68, 75, 82, 89, 97, 105, 113, 122, 131, 140, 150, 160, 170, 181, 192, 203, 215, 227, 239, 252, 265, 278, 292, 306, 320, 335
OFFSET
0,3
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
Sequence in context: A029006 A085756 A350896 * A029005 A132154 A049807
KEYWORD
nonn
STATUS
approved