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 A047620 #25 Sep 08 2022 08:44:57
%S A047620 0,1,2,5,8,9,10,13,16,17,18,21,24,25,26,29,32,33,34,37,40,41,42,45,48,
%T A047620 49,50,53,56,57,58,61,64,65,66,69,72,73,74,77,80,81,82,85,88,89,90,93,
%U A047620 96,97,98,101,104,105,106,109,112,113,114,117,120,121,122
%N A047620 Numbers that are congruent to {0, 1, 2, 5} mod 8.
%H A047620 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1).
%F A047620 From _R. J. Mathar_, Oct 08 2011: (Start)
%F A047620 G.f.: x^2*(1+3*x^2) / ( (x^2+1)*(x-1)^2 ).
%F A047620 a(n) = 2*n-3+sin(n*Pi/2). (End)
%F A047620 From _Wesley Ivan Hurt_, May 22 2016: (Start)
%F A047620 a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.
%F A047620 a(n) = (4n-6+I^(1-n)-I^(1+n))/2 where i=sqrt(-1).
%F A047620 a(2n+2) = A016813(n) n>0, a(2n-1) = A047467(n). (End)
%F A047620 Sum_{n>=2} (-1)^n/a(n) = Pi/16 + 5*log(2)/8. - _Amiram Eldar_, Dec 19 2021
%p A047620 A047620:=n->(4*n-6+I^(1-n)-I^(1+n))/2: seq(A047620(n), n=1..100); # _Wesley Ivan Hurt_, May 22 2016
%t A047620 Table[(4n-6+I^(1-n)-I^(1+n))/2, {n, 80}] (* _Wesley Ivan Hurt_, May 22 2016 *)
%t A047620 LinearRecurrence[{2,-2,2,-1},{0,1,2,5},120] (* _Harvey P. Dale_, Mar 11 2017 *)
%o A047620 (Sage) [lucas_number1(n,0,1)+2*n-3 for n in range(1,57)] # _Zerinvary Lajos_, Jul 06 2008
%o A047620 (Magma) [n : n in [0..150] | n mod 8 in [0, 1, 2, 5]]; // _Wesley Ivan Hurt_, May 22 2016
%Y A047620 Cf. A016813, A047404, A047431, A047467, A047546, A047557, A047578, A056594.
%K A047620 nonn,easy
%O A047620 1,3
%A A047620 _N. J. A. Sloane_
%E A047620 More terms from _Wesley Ivan Hurt_, May 22 2016