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 A047424 #26 Sep 08 2022 08:44:57
%S A047424 0,2,3,4,5,6,8,10,11,12,13,14,16,18,19,20,21,22,24,26,27,28,29,30,32,
%T A047424 34,35,36,37,38,40,42,43,44,45,46,48,50,51,52,53,54,56,58,59,60,61,62,
%U A047424 64,66,67,68,69,70,72,74,75,76,77,78,80,82,83,84,85,86
%N A047424 Numbers that are congruent to {0, 2, 3, 4, 5, 6} mod 8.
%H A047424 G. C. Greubel, <a href="/A047424/b047424.txt">Table of n, a(n) for n = 1..1000</a>
%H A047424 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-2,2,-1).
%F A047424 G.f.: x^2*(2-x+2*x^2-x^3+2*x^4) / ( (1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - _R. J. Mathar_, Oct 08 2011
%F A047424 From _Wesley Ivan Hurt_, Jun 15 2016: (Start)
%F A047424 a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-2*a(n-4)+2*a(n-5)-a(n-6) for n>6.
%F A047424 a(n) = (12*n-12-sqrt(3)*cos((1-4*n)*Pi/6)-3*sqrt(3)*cos((1+2*n)*Pi/6))/9.
%F A047424 a(6k) = 8k-2, a(6k-1) = 8k-3, a(6k-2) = 8k-4, a(6k-3) = 8k-5, a(6k-4) = 8k-6, a(6k-5) = 8k-8. (End)
%F A047424 Sum_{n>=2} (-1)^n/a(n) = sqrt(2)*log(3+2*sqrt(2))/8. - _Amiram Eldar_, Dec 27 2021
%p A047424 A047424:=n->(12*n-12-sqrt(3)*cos((1-4*n)*Pi/6)-3*sqrt(3)*cos((1+2*n)*Pi/6))/9: seq(A047424(n), n=1..100); # _Wesley Ivan Hurt_, Jun 15 2016
%t A047424 Select[Range[0,100], MemberQ[{0,2,3,4,5,6}, Mod[#,8]]&] (* _Harvey P. Dale_, Mar 21 2011 *)
%o A047424 (Magma) [n : n in [0..100] | n mod 8 in [0] cat [2..6]]; // _Wesley Ivan Hurt_, Jun 15 2016
%o A047424 (PARI) my(x='x+O('x^50)); concat([0], Vec(x^2*(2 -x +2*x^2 -x^3 +2*x^4 )/((1 + x+x^2)*(x^2-x+1)*(x-1)^2))) \\ _G. C. Greubel_, Oct 29 2017
%Y A047424 Cf. A047428, A047503.
%K A047424 nonn,easy
%O A047424 1,2
%A A047424 _N. J. A. Sloane_