cp's OEIS Frontend

A008816 Expansion of (1+x^9)/((1-x)^2*(1-x^9)).

%I A008816 #11 Sep 08 2022 08:44:36
%S A008816 1,2,3,4,5,6,7,8,9,12,15,18,21,24,27,30,33,36,41,46,51,56,61,66,71,76,
%T A008816 81,88,95,102,109,116,123,130,137,144,153,162,171,180,189,198,207,216,
%U A008816 225,236,247,258,269,280,291,302,313,324,337,350,363,376,389,402
%N A008816 Expansion of (1+x^9)/((1-x)^2*(1-x^9)).
%H A008816 G. C. Greubel, <a href="/A008816/b008816.txt">Table of n, a(n) for n = 0..1000</a>
%H A008816 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,1,-2,1).
%F A008816 G.f.: (1+x^9)/((1-x)^2*(1-x^9)). - _G. C. Greubel_, Sep 12 2019
%p A008816 seq(coeff(series((1+x^9)/((1-x)^2*(1-x^9)), x, n+1), x, n), n = 0..50); # _G. C. Greubel_, Sep 12 2019
%t A008816 LinearRecurrence[{2,-1,0,0,0,0,0,0,1,-2,1}, {1,2,3,4,5,6,7,8,9,12,15}, 70] (* or *) CoefficientList[Series[(1+x^9)/((1-x)^2*(1-x^9)), {x,0, 70}], x] (* _G. C. Greubel_, Sep 12 2019 *)
%o A008816 (PARI) my(x='x+O('x^70)); Vec((1+x^9)/((1-x)^2*(1-x^9))) \\ _G. C. Greubel_, Sep 12 2019
%o A008816 (Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^9)/((1-x)^2*(1-x^9)) )); // _G. C. Greubel_, Sep 12 2019
%o A008816 (Sage)
%o A008816 def A008815_list(prec):
%o A008816     P.<x> = PowerSeriesRing(ZZ, prec)
%o A008816     return P((1+x^8)/((1-x)^2*(1-x^8))).list()
%o A008816 A008815_list(70) # _G. C. Greubel_, Sep 12 2019
%o A008816 (GAP) a:=[1,2,3,4,5,6,7,8,9,12,15];; for n in [12..70] do a[n]:=2*a[n-1] -a[n-2]+a[n-9]-2*a[n-10]+a[n-11]; od; a; # _G. C. Greubel_, Sep 12 2019
%Y A008816 Cf. Expansions of the form (1+x^m)/((1-x)^2*(1-x^m)): A000290 (m=1), A000982 (m=2), A008810 (m=3), A008811 (m=4), A008812 (m=5), A008813 (m=6), A008814 (m=7), A008815 (m=8), this sequence (m=9), A008817 (m=10).
%K A008816 nonn
%O A008816 0,2
%A A008816 _N. J. A. Sloane_
%E A008816 More terms added by _G. C. Greubel_, Sep 12 2019