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 A113854 #13 May 11 2025 13:13:16
%S A113854 1,3,35,99,227,2275,6371,14563,145635,407779,932067,9320675,26097891,
%T A113854 59652323,596523235,1670265059,3817748707,38177487075,106896963811,
%U A113854 244335917283,2443359172835,6841405683939,15637498706147
%N A113854 a(n) = sum(2^(A047240(i)-1), i=1..n).
%H A113854 Vincenzo Librandi, <a href="/A113854/b113854.txt">Table of n, a(n) for n = 1..300</a>
%H A113854 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,64,-64).
%F A113854 G.f.: x*(1+2*x+32*x^2)/((-1+x)*(-1+4*x)*(1+4*x+16*x^2)). - _Vaclav Kotesovec_, Nov 28 2012
%e A113854 a(2) = 2^(A047240(1)-1) + 2^(A047240(2)-1) = 2^0 + 2^1 = 3
%t A113854 a = {}; s = 0; For[n = 1, n < 48, n++, If[Length[Intersection[{Mod[n, 6]}, {1, 2, 0}]] > 0, s = s + 2^(n - 1); AppendTo[a, s]]]; a
%t A113854 CoefficientList[Series[(1 + 2 x + 32 x^2)/((-1 + x) (-1 + 4 x) (1 + 4 x + 16 x^2)), {x, 0, 25}], x] (* _Vincenzo Librandi_, May 20 2013 *)
%t A113854 LinearRecurrence[{1,0,64,-64},{1,3,35,99},30] (* _Harvey P. Dale_, May 11 2025 *)
%Y A113854 Cf. A047240.
%K A113854 nonn,easy
%O A113854 1,2
%A A113854 _Artur Jasinski_, Jan 27 2006
%E A113854 Edited by _Stefan Steinerberger_, Jul 24 2007