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 A047401 #38 Mar 20 2023 15:15:57
%S A047401 0,1,3,6,8,9,11,14,16,17,19,22,24,25,27,30,32,33,35,38,40,41,43,46,48,
%T A047401 49,51,54,56,57,59,62,64,65,67,70,72,73,75,78,80,81,83,86,88,89,91,94,
%U A047401 96,97,99,102,104,105,107,110,112,113,115,118,120,121,123
%N A047401 Numbers that are congruent to {0, 1, 3, 6} mod 8.
%C A047401 Partial sums of A068073. - _Jeremy Gardiner_, Jul 20 2013.
%H A047401 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1).
%F A047401 G.f.: x^2*(1+x+2*x^2) / ( (x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 05 2011
%F A047401 a(n) = 2*(n-1)+(i^(n*(n-1))-1)/2, where i=sqrt(-1). - _Bruno Berselli_, Dec 05 2011
%F A047401 From _Wesley Ivan Hurt_, Jun 01 2016: (Start)
%F A047401 a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.
%F A047401 a(2k) = A047452(k), a(2k-1) = A047470(k). (End)
%F A047401 Sum_{n>=2} (-1)^n/a(n) = Pi/16 + (3-sqrt(2))*log(2)/8 + sqrt(2)*log(2+sqrt(2))/4. - _Amiram Eldar_, Dec 20 2021
%p A047401 A047401:=n->2*(n-1)+(I^(n*(n-1))-1)/2: seq(A047401(n), n=1..100); # _Wesley Ivan Hurt_, Jun 01 2016
%t A047401 Select[Range[0,107], MemberQ[{0, 1, 3, 6}, Mod[#, 8]]&] (* _Bruno Berselli_, Dec 05 2011 *)
%o A047401 (Maxima) makelist(2*(n-1)+(%i^(n*(n-1))-1)/2,n,1,55); /* _Bruno Berselli_, Dec 05 2011 */
%o A047401 (Magma) [n : n in [0..150] | n mod 8 in [0, 1, 3, 6]]; // _Wesley Ivan Hurt_, Jun 01 2016
%o A047401 (PARI) my(x='x+O('x^100)); concat(0, Vec(x^2*(1+x+2*x^2)/((x^2+1)*(x-1)^2))) \\ _Altug Alkan_, Jun 02 2016
%Y A047401 Cf. A047452, A047470, A068073.
%K A047401 nonn,easy
%O A047401 1,3
%A A047401 _N. J. A. Sloane_