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 A047322 #32 Sep 08 2022 08:44:56
%S A047322 0,1,5,6,7,8,12,13,14,15,19,20,21,22,26,27,28,29,33,34,35,36,40,41,42,
%T A047322 43,47,48,49,50,54,55,56,57,61,62,63,64,68,69,70,71,75,76,77,78,82,83,
%U A047322 84,85,89,90,91,92,96,97,98,99,103,104,105,106,110,111
%N A047322 Numbers that are congruent to {0, 1, 5, 6} mod 7.
%H A047322 Vincenzo Librandi, <a href="/A047322/b047322.txt">Table of n, a(n) for n = 1..1000</a>
%H A047322 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047322 a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(1)=5, b(k)=7*2^(k-2) for k>1. - _Philippe Deléham_, Oct 19 2011
%F A047322 G.f.: x^2*(1+4*x+x^2+x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 03 2011
%F A047322 From _Wesley Ivan Hurt_, May 23 2016: (Start)
%F A047322 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047322 a(n) = (14n-11-3*I^(2n)+(3-3*I)*I^(-n)+(3+3*I)*I^n)/8 where I=sqrt(-1).
%F A047322 a(2n) = A047336(n), a(2n-1) = A047382(n). (End)
%F A047322 E.g.f.: (4 - 3*sin(x) + 3*cos(x) + (7*x - 4)*sinh(x) + 7*(x - 1)*cosh(x))/4. - _Ilya Gutkovskiy_, May 24 2016
%p A047322 A047322:=n->(14*n-11-3*I^(2*n)+(3-3*I)*I^(-n)+(3+3*I)*I^n)/8: seq(A047322(n), n=1..100); # _Wesley Ivan Hurt_, May 23 2016
%t A047322 Table[(14n-11-3*I^(2n)+(3-3*I)*I^(-n)+(3+3*I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, May 23 2016 *)
%t A047322 LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 5, 6, 7}, 60] (* _Vincenzo Librandi_, May 24 2016 *)
%o A047322 (Magma) [n : n in [0..150] | n mod 7 in [0, 1, 5, 6]]; // _Wesley Ivan Hurt_, May 23 2016
%Y A047322 Cf. A030308, A047336, A047382.
%K A047322 nonn,easy
%O A047322 1,3
%A A047322 _N. J. A. Sloane_
%E A047322 More terms from _Wesley Ivan Hurt_, May 23 2016