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 A008813 #23 Sep 08 2022 08:44:36
%S A008813 1,2,3,4,5,6,9,12,15,18,21,24,29,34,39,44,49,54,61,68,75,82,89,96,105,
%T A008813 114,123,132,141,150,161,172,183,194,205,216,229,242,255,268,281,294,
%U A008813 309,324,339,354,369,384,401,418,435,452,469,486,505,524,543,562
%N A008813 Expansion of (1+x^6)/((1-x)^2*(1-x^6)).
%C A008813 Number of 0..n arrays of 7 elements with zero second differences. - _R. H. Hardin_, Nov 16 2011
%H A008813 G. C. Greubel, <a href="/A008813/b008813.txt">Table of n, a(n) for n = 0..1000</a>
%H A008813 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,1,-2,1).
%F A008813 G.f.: (1+x^6)/((1-x)^2*(1-x^6)).
%F A008813 a(n) = 2*a(n-1) -a(n-2) +a(n-6) -2*a(n-7) +a(n-8). - _R. H. Hardin_, Nov 16 2011
%p A008813 seq(coeff(series((1+x^6)/((1-x)^2*(1-x^6)), x, n+1), x, n), n = 0..70); # _G. C. Greubel_, Sep 12 2019
%t A008813 CoefficientList[Series[(1+x^6)/(1-x)^2/(1-x^6), {x,0,70}], x] (* or *) LinearRecurrence[{2,-1,0,0,0,1,-2,1}, {1,2,3,4,5,6,9,12}, 70] (* _Harvey P. Dale_, Oct 13 2012 *)
%o A008813 (PARI) Vec((1+x^6)/((1-x)^2*(1-x^6)) +O(x^70)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o A008813 (Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^6)/((1-x)^2*(1-x^6)) )); // _G. C. Greubel_, Sep 12 2019
%o A008813 (Sage)
%o A008813 def A008813_list(prec):
%o A008813 P.<x> = PowerSeriesRing(ZZ, prec)
%o A008813 return P((1+x^6)/((1-x)^2*(1-x^6))).list()
%o A008813 A008813_list(70) # _G. C. Greubel_, Sep 12 2019
%o A008813 (GAP) a:=[1,2,3,4,5,6,9,12];; for n in [9..70] do a[n]:=2*a[n-1]-a[n-2] +a[n-6]-2*a[n-7]+a[n-8]; od; a; # _G. C. Greubel_, Sep 12 2019
%Y A008813 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), this sequence (m=6), A008814 (m=7), A008815 (m=8), A008816 (m=9), A008817 (m=10).
%K A008813 nonn,easy
%O A008813 0,2
%A A008813 _N. J. A. Sloane_
%E A008813 More terms added by _G. C. Greubel_, Sep 12 2019