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 A047569 #20 Feb 15 2024 18:10:17
%S A047569 0,1,4,5,6,7,8,9,12,13,14,15,16,17,20,21,22,23,24,25,28,29,30,31,32,
%T A047569 33,36,37,38,39,40,41,44,45,46,47,48,49,52,53,54,55,56,57,60,61,62,63,
%U A047569 64,65,68,69,70,71,72,73,76,77,78,79,80,81,84,85,86,87,88
%N A047569 Numbers that are congruent to {0, 1, 4, 5, 6, 7} mod 8.
%H A047569 Colin Barker, <a href="/A047569/b047569.txt">Table of n, a(n) for n = 1..1000</a>
%H A047569 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A047569 G.f.: x^2*(1+3*x+x^2+x^3+x^4+x^5) / ((1-x)^2*(1+x)*(1-x+x^2)*(1+x+x^2)). - _Colin Barker_, Jan 09 2016
%F A047569 From _Wesley Ivan Hurt_, Jun 16 2016: (Start)
%F A047569 a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
%F A047569 a(n) = (24*n-15-3*cos(n*Pi)+4*sqrt(3)*cos((1-4*n)*Pi/6)-12*sin((1+2*n)*Pi/6))/18.
%F A047569 a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-4, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)
%F A047569 Sum_{n>=2} (-1)^n/a(n) = (2-sqrt(2))*Pi/16 + (14-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8. - _Amiram Eldar_, Dec 27 2021
%p A047569 A047569:=n->(24*n-15-3*cos(n*Pi)+4*sqrt(3)*cos((1-4*n)*Pi/6)-12*sin((1+2*n)*Pi/6))/18: seq(A047569(n), n=1..100); # _Wesley Ivan Hurt_, Jun 16 2016
%t A047569 Select[Range[0, 100], MemberQ[{0, 1, 4, 5, 6, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 16 2016 *)
%t A047569 LinearRecurrence[{1,0,0,0,0,1,-1},{0,1,4,5,6,7,8},80] (* _Harvey P. Dale_, Feb 15 2024 *)
%o A047569 (PARI) concat(0, Vec(x^2*(1+3*x+x^2+x^3+x^4+x^5)/((1-x)^2*(1+x)*(1-x+x^2)*(1+x+x^2)) + O(x^100))) \\ _Colin Barker_, Jan 09 2016
%Y A047569 Cf. A047517, A047585.
%K A047569 nonn,easy
%O A047569 1,3
%A A047569 _N. J. A. Sloane_