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 A047294 #35 Sep 08 2022 08:44:56
%S A047294 1,2,4,6,8,9,11,13,15,16,18,20,22,23,25,27,29,30,32,34,36,37,39,41,43,
%T A047294 44,46,48,50,51,53,55,57,58,60,62,64,65,67,69,71,72,74,76,78,79,81,83,
%U A047294 85,86,88,90,92,93,95,97,99,100,102,104,106,107,109,111
%N A047294 Numbers that are congruent to {1, 2, 4, 6} mod 7.
%H A047294 Vincenzo Librandi, <a href="/A047294/b047294.txt">Table of n, a(n) for n = 1..5000</a>
%H A047294 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047294 a(n) = ceiling(floor((7*n - 5)/2)/2).
%F A047294 From _Colin Barker_, Mar 14 2012: (Start)
%F A047294 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047294 G.f.: x*(1 + x + 2*x^2 + 2*x^3 + x^4)/((1-x)^2*(1+x)*(1+x^2)). (End)
%F A047294 a(n) = (-9 -(-1)^n + (1+i)*(-i)^n + (1-i)*i^n + 14*n)/8 where i=sqrt(-1). - _Colin Barker_, May 14 2012
%F A047294 a(2k) = A047276(k), a(2k-1) = A047346(k). - _Wesley Ivan Hurt_, Jun 01 2016
%F A047294 E.g.f.: (4 + sin(x) + cos(x) + (7*x - 4)*sinh(x) + (7*x - 5)*cosh(x))/4. - _Ilya Gutkovskiy_, Jun 01 2016
%p A047294 A047294:=n->ceil(floor((7*n-5)/2)/2): seq(A047294(n), n=1..100); # _Wesley Ivan Hurt_, Jun 01 2016
%t A047294 Select[Range[0,100], MemberQ[{1,2,4,6}, Mod[#,7]]&] (* _Vincenzo Librandi_, Apr 27 2012 *)
%t A047294 LinearRecurrence[{1,0,0,1,-1},{1,2,4,6,8},100] (* _G. C. Greubel_, Jun 01 2016 *)
%o A047294 (Magma) I:=[1, 2, 4, 6, 8]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // _Vincenzo Librandi_, Apr 27 2012
%o A047294 (PARI) x='x+O('x^100); Vec(x*(1+x+2*x^2+2*x^3+x^4)/((1-x)^2*(1+x)*(1+x^2))) \\ _Altug Alkan_, Dec 24 2015
%Y A047294 Cf. A047276, A047346.
%K A047294 nonn,easy
%O A047294 1,2
%A A047294 _N. J. A. Sloane_