This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A008817 #16 Sep 08 2022 08:44:36
%S A008817 1,2,3,4,5,6,7,8,9,10,13,16,19,22,25,28,31,34,37,40,45,50,55,60,65,70,
%T A008817 75,80,85,90,97,104,111,118,125,132,139,146,153,160,169,178,187,196,
%U A008817 205,214,223,232,241,250,261,272,283,294,305,316,327,338,349,360
%N A008817 Expansion of (1+x^10)/((1-x)^2*(1-x^10)).
%H A008817 G. C. Greubel, <a href="/A008817/b008817.txt">Table of n, a(n) for n = 0..1000</a>
%H A008817 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,0,1,-2,1).
%F A008817 G.f.: (1+x^10)/((1-x)^2*(1-x^10)).
%F A008817 a(0)=1, a(1)=2, a(2)=3, a(3)=4, a(4)=5, a(5)=6, a(6)=7, a(7)=8, a(8)=9, a(9)=10, a(10)=13, a(11)=16, a(n) = 2*a(n-1) - a(n-2) + a(n-10) - 2*a(n-11) + a(n-12). - _Harvey P. Dale_, Jul 31 2014
%p A008817 seq(coeff(series((1+x^10)/((1-x)^2*(1-x^10)), x, n+1), x, n), n = 0..80); # _G. C. Greubel_, Sep 12 2019
%t A008817 CoefficientList[Series[(1+x^10)/(1-x)^2/(1-x^10), {x,0,80}], x] (* or *) LinearRecurrence[{2,-1,0,0,0,0,0,0,0,1,-2,1}, {1,2,3,4,5,6,7,8,9,10, 13,16}, 80] (* _Harvey P. Dale_, Jul 31 2014 *)
%o A008817 (PARI) my(x='x+O('x^80)); Vec((1+x^10)/((1-x)^2*(1-x^10))) \\ _G. C. Greubel_, Sep 12 2019
%o A008817 (Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^10)/((1-x)^2*(1-x^10)) )); // _G. C. Greubel_, Sep 12 2019
%o A008817 (Sage)
%o A008817 def A008817_list(prec):
%o A008817 P.<x> = PowerSeriesRing(ZZ, prec)
%o A008817 return P((1+x^10)/((1-x)^2*(1-x^10))).list()
%o A008817 A008817_list(80) # _G. C. Greubel_, Sep 12 2019
%o A008817 (GAP) a:=[1,2,3,4,5,6,7,8,9,10, 13,16];; for n in [13..80] do a[n]:=2*a[n-1]-a[n-2]+a[n-10]-2*a[n-11]+a[n-12]; od; a; # _G. C. Greubel_, Sep 12 2019
%Y A008817 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), A008816 (m=9), this sequence (m=10).
%K A008817 nonn
%O A008817 0,2
%A A008817 _N. J. A. Sloane_