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 A047344 #28 Sep 08 2022 08:44:57
%S A047344 0,1,3,4,7,8,10,11,14,15,17,18,21,22,24,25,28,29,31,32,35,36,38,39,42,
%T A047344 43,45,46,49,50,52,53,56,57,59,60,63,64,66,67,70,71,73,74,77,78,80,81,
%U A047344 84,85,87,88,91,92,94,95,98,99,101,102,105,106,108,109
%N A047344 Numbers that are congruent to {0, 1, 3, 4} mod 7.
%H A047344 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047344 a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(1)=3 and b(k)=7*2^(k-2) for k>1. - _Philippe Deléham_, Oct 17 2011
%F A047344 G.f.: x^2*(1+2*x+x^2+3*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 04 2011
%F A047344 From _Wesley Ivan Hurt_, May 23 2016: (Start)
%F A047344 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047344 a(n) = (14n-19-3*i^(2n)-(1-i)*i^(-n)-(1+i)*i^n)/8 where i=sqrt(-1).
%F A047344 a(2n) = A047346(n), a(2n-1) = A047355(n). (End)
%F A047344 E.g.f.: (12 + sin(x) - cos(x) + (7*x - 8)*sinh(x) + (7*x - 11)*cosh(x))/4. - _Ilya Gutkovskiy_, May 24 2016
%p A047344 A047344:=n->(14*n-19-3*I^(2*n)-(1-I)*I^(-n)-(1+I)*I^n)/8: seq(A047344(n), n=1..100); # _Wesley Ivan Hurt_, May 23 2016
%t A047344 Table[(14n-19-3*I^(2n)-(1-I)*I^(-n)-(1+I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, May 23 2016 *)
%t A047344 LinearRecurrence[{1,0,0,1,-1},{0,1,3,4,7},80] (* _Harvey P. Dale_, May 06 2021 *)
%o A047344 (PARI) forstep(n=0,200,[1,2,1,3],print1(n", ")) \\ _Charles R Greathouse IV_, Oct 17 2011
%o A047344 (Magma) [n : n in [0..150] | n mod 7 in [0, 1, 3, 4]]; // _Wesley Ivan Hurt_, May 23 2016
%Y A047344 Cf. A030308, A047346, A047355.
%K A047344 nonn,easy
%O A047344 1,3
%A A047344 _N. J. A. Sloane_
%E A047344 More terms from _Wesley Ivan Hurt_, May 23 2016