(MAGMAMagma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^16)/((1-x)*(1-x^2)*(1-x^3)) )); //G. C. Greubel,Aug 09 2019

proposed

approved

editing

proposed

G. C. Greubel, <a href= "/A008759/b008759.txt ">Table of n, a(n) for n = 0..1000</a>

<a href= "/index/Rec#order_06" >Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1).

seq(coeff(series((1+x^16)/((1-x)*(1-x^2)*(1-x^3)), x, n+1), x, n), n = 1.. 60); #G. C. Greubel,Aug 09 2019

Join[{1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14}, LinearRecurrence[{1, 1, 0, -1, -1, 1}, {16, 19, 21, 24, 27, 31}, 48]] (*G. C. Greubel,Aug 09 2019 *)

(PARI) my(x='x+O('x^60)); Vec((1+x^16)/((1-x)*(1-x^2)*(1-x^3))) \\G. C. Greubel,Aug 09 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^16)/((1-x)*(1-x^2)*(1-x^3)) )); //G. C. Greubel,Aug 09 2019

(Sage)

defA008759_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P( (1+x^16)/((1-x)*(1-x^2)*(1-x^3)) ).list()

A008759_list(60) #G. C. Greubel,Aug 09 2019

(GAP) a:=[16, 19, 21, 24, 27, 31];; for n in [7..60] do a[n]:=a[n-1]+a[n-2]-a[n-4] -a[n-5]+a[n-6]; od; Concatenation([1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14], a); #G. C. Greubel,Aug 09 2019

N. J. A. Sloane.

approved

editing

editing

approved

<a href= "/index/Rec#order_06" >Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, -1, -1, 1).

approved

editing

editing

approved

CoefficientList[Series[(1+x^16)/(1-x)/(1-x^2)/(1-x^3), {x, 0, 60}], x] (*Harvey P. Dale,Sep 19 2016 *)

approved

editing

_N. J. A. Sloane(njas(AT)research.att.com)_.

nonn,new

nonn

N.J.A.Sloane(njas(AT)research.att.com).