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 A047291 #33 Sep 08 2022 08:44:56
%S A047291 0,1,4,6,7,8,11,13,14,15,18,20,21,22,25,27,28,29,32,34,35,36,39,41,42,
%T A047291 43,46,48,49,50,53,55,56,57,60,62,63,64,67,69,70,71,74,76,77,78,81,83,
%U A047291 84,85,88,90,91,92,95,97,98,99,102,104,105,106,109,111
%N A047291 Numbers that are congruent to {0, 1, 4, 6} mod 7.
%H A047291 Vincenzo Librandi, <a href="/A047291/b047291.txt">Table of n, a(n) for n = 1..5000</a>
%H A047291 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047291 From _Colin Barker_, Mar 13 2012: (Start)
%F A047291 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047291 G.f.: x^2*(1 + 3*x + 2*x^2 + x^3)/((1-x)^2*(1+x)*(1+x^2)). (End)
%F A047291 a(n) = (-13 - (-1)^n + (3-i)*(-i)^n + (3+i)*i^n + 14*n)/8 where i=sqrt(-1). - _Colin Barker_, May 14 2012
%F A047291 a(2k) = A047336(k), a(2k-1) = A047345(k). - _Wesley Ivan Hurt_, Jun 01 2016
%F A047291 E.g.f.: (4 - sin(x) + 3*cos(x) + (7*x - 6)*sinh(x) + 7*(x - 1)*cosh(x))/4. - _Ilya Gutkovskiy_, Jun 01 2016
%p A047291 A047291:=n->(-13-(-1)^n+(3-I)*(-I)^n+(3+I)*I^n+14*n)/8: seq(A047291(n), n=1..100); # _Wesley Ivan Hurt_, Jun 01 2016
%t A047291 Select[Range[0,120], MemberQ[{0,1,4,6}, Mod[#,7]]&] (* _Vincenzo Librandi_, Apr 26 2012 *)
%t A047291 LinearRecurrence[{1,0,0,1,-1},{0,1,4,6,7},100] (* _G. C. Greubel_, Jun 01 2016 *)
%o A047291 (Magma) I:=[0, 1, 4, 6, 7]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // _Vincenzo Librandi_, Apr 26 2012
%o A047291 (PARI) x='x+O('x^100); concat(0, Vec(x^2*(1+3*x+2*x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)))) \\ _Altug Alkan_, Dec 24 2015
%Y A047291 Cf. A047336, A047345.
%K A047291 nonn,easy
%O A047291 1,3
%A A047291 _N. J. A. Sloane_