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 A047397 #26 Sep 08 2022 08:44:57
%S A047397 0,1,2,6,8,9,10,14,16,17,18,22,24,25,26,30,32,33,34,38,40,41,42,46,48,
%T A047397 49,50,54,56,57,58,62,64,65,66,70,72,73,74,78,80,81,82,86,88,89,90,94,
%U A047397 96,97,98,102,104,105,106,110,112,113,114,118,120,121,122
%N A047397 Numbers that are congruent to {0, 1, 2, 6} mod 8.
%H A047397 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047397 G.f.: x^2*(1+x+4*x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 05 2011
%F A047397 From _Wesley Ivan Hurt_, May 24 2016: (Start)
%F A047397 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047397 a(n) = (8*n-11+i^(2*n)+(1+2*i)*i^(-n)+(1-2*i)*i^n)/4, where i=sqrt(-1).
%F A047397 a(2k) = A047452(k), a(2k-1) = A047467(k). (End)
%F A047397 E.g.f.: (4 + 2*sin(x) + cos(x) + (4*x - 6)*sinh(x) + (4*x - 5)*cosh(x))/2. - _Ilya Gutkovskiy_, May 25 2016
%F A047397 Sum_{n>=2} (-1)^n/a(n) = (sqrt(2)-1)*Pi/16 + log(2)/2 + sqrt(2)*log(sqrt(2)+1)/8. - _Amiram Eldar_, Dec 20 2021
%p A047397 A047397:=n->(8*n-11+I^(2*n)+(1+2*I)*I^(-n)+(1-2*I)*I^n)/4: seq(A047397(n), n=1..100); # _Wesley Ivan Hurt_, May 24 2016
%t A047397 Table[(8n-11+I^(2n)+(1+2*I)*I^(-n)+(1-2*I)*I^n)/4, {n, 80}] (* _Wesley Ivan Hurt_, May 24 2016 *)
%t A047397 LinearRecurrence[{1,0,0,1,-1},{0,1,2,6,8},70] (* _Harvey P. Dale_, Dec 31 2017 *)
%o A047397 (Magma) [n : n in [0..150] | n mod 8 in [0, 1, 2, 6]]; // _Wesley Ivan Hurt_, May 24 2016
%Y A047397 Cf. A047452, A047467.
%K A047397 nonn,easy
%O A047397 1,3
%A A047397 _N. J. A. Sloane_
%E A047397 More terms from _Wesley Ivan Hurt_, May 24 2016