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Expansion of (1+2*x^9+x^16)/((1-x^2)^2*(1-x^16)).
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%I #17 Sep 08 2022 08:44:36

%S 1,0,2,0,3,0,4,0,5,2,6,4,7,6,8,8,11,10,14,12,17,14,20,16,23,20,26,24,

%T 29,28,32,32,37,36,42,40,47,44,52,48,57,54,62,60,67,66,72,72,79,78,86,

%U 84,93,90,100,96,107,104,114,112,121,120,128,128,137,136

%N Expansion of (1+2*x^9+x^16)/((1-x^2)^2*(1-x^16)).

%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1).

%F G.f.: (1+2*x^9+x^16)/((1-x^2)^2*(1-x^16)). - _G. C. Greubel_, Sep 13 2019

%F G.f.: (1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8+x^9-x^10+x^11-x^12+x^13-x^14+x^15)/((1-x)^3*(1+x)^2*(1+x^2)*(1+x^4)*(1+x^8)). - _R. J. Mathar_, Feb 04 2022

%p seq(coeff(series((1+2*x^9+x^16)/((1-x^2)^2*(1-x^16)), x, n+1), x, n), n = 0..75); # _G. C. Greubel_, Sep 13 2019

%t CoefficientList[Series[(1+2*x^9+x^16)/((1-x^2)^2*(1-x^16)), {x,0,75}], x] (* or *) LinearRecurrence[{1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1}, {1,0,2,0,3,0,4,0,5,2,6,4,7,6,8,8,11,10,14}, 75] (* _G. C. Greubel_, Sep 13 2019 *)

%o (PARI) my(x='x+O('x^75)); Vec((1+2*x^9+x^16)/((1-x^2)^2*(1-x^16))) \\ _G. C. Greubel_, Sep 13 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 75); Coefficients(R!( (1+2*x^9+x^16)/((1-x^2)^2*(1-x^16)) )); // _G. C. Greubel_, Sep 13 2019

%o (Sage)

%o def A008821_list(prec):

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

%o return P((1+2*x^9+x^16)/((1-x^2)^2*(1-x^16))).list()

%o A008821_list(75) # _G. C. Greubel_, Sep 13 2019

%o (GAP) a:=[1,0,2,0,3,0,4,0,5,2,6,4,7,6,8,8,11,10,14];; for n in [20..75] do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-16]-a[n-17]-a[n-18]+a[n-19]; od; a; # _G. C. Greubel_, Sep 13 2019

%Y Expansions of the form (1 +2*x^(2*m+1) +x^(4*m))/((1-x^2)^2*(1-x^(4*m))): A008818 (m=1), A008819 (m=2), A008820 (m=3), this sequence (m=4).

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_

%E More terms added by _G. C. Greubel_, Sep 13 2019