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 A047269 #41 Jan 03 2025 14:48:57
%S A047269 0,1,2,5,6,7,8,11,12,13,14,17,18,19,20,23,24,25,26,29,30,31,32,35,36,
%T A047269 37,38,41,42,43,44,47,48,49,50,53,54,55,56,59,60,61,62,65,66,67,68,71,
%U A047269 72,73,74,77,78,79,80,83,84,85,86,89,90,91,92,95,96,97
%N A047269 Numbers that are congruent to {0, 1, 2, 5} mod 6.
%H A047269 Vincenzo Librandi, <a href="/A047269/b047269.txt">Table of n, a(n) for n = 1..1000</a>
%H A047269 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047269 From _Colin Barker_, May 14 2012: (Start)
%F A047269 a(n) = (-7+(-1)^n+(1+i)*(-i)^n+(1-i)*i^n+6*n)/4 where i=sqrt(-1).
%F A047269 G.f.: x^2*(1+x+3*x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)). (End)
%F A047269 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - _Vincenzo Librandi_, May 15 2012
%F A047269 a(2n) = A007310(n), a(2n-1) = A047238(n). - _Wesley Ivan Hurt_, May 22 2016
%F A047269 Sum_{n>=2} (-1)^n/a(n) = log(3)/4 + 2*log(2)/3 - sqrt(3)*Pi/36. - _Amiram Eldar_, Dec 16 2021
%F A047269 a(n) = n - 1 + 2*floor(n/4). - _Taras Goy_, Jan 03 2025
%p A047269 A047269:=n->(-7+(-1)^n+(1+I)*(-I)^n+(1-I)*I^n+6*n)/4: seq(A047269(n), n=1..100); # _Wesley Ivan Hurt_, May 22 2016
%t A047269 Select[Range[0,4000], MemberQ[{0,1,2,5}, Mod[#,6]]&] (* _Vincenzo Librandi_, May 15 2012 *)
%t A047269 LinearRecurrence[{1,0,0,1,-1},{0,1,2,5,6},80] (* _Harvey P. Dale_, Jun 21 2022 *)
%o A047269 (Magma) I:=[0, 1, 2, 5, 6]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // _Vincenzo Librandi_, May 15 2012
%o A047269 (PARI) x='x+O('x^100); concat(0, Vec(x^2*(1+x+3*x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)))) \\ _Altug Alkan_, Dec 24 2015
%Y A047269 Cf. A007310, A047238.
%K A047269 nonn,easy
%O A047269 1,3
%A A047269 _N. J. A. Sloane_