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 A191497 #19 Feb 19 2025 02:41:20
%S A191497 0,0,0,0,1,2,4,8,15,30,60,120,241,482,964,1928,3855,7710,15420,30840,
%T A191497 61681,123362,246724,493448,986895,1973790,3947580,7895160,15790321,
%U A191497 31580642,63161284,126322568,252645135
%N A191497 a(n+1) = 2*a(n) + A014017(n+5), a(0) = 0.
%H A191497 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,-1,2).
%F A191497 a(n+4) = 2^n - a(n).
%F A191497 a(n) = 2*a(n-1) - a(n-4) + 2*a(n-5).
%F A191497 a(4*n+4) = 16*a(4*n) + (-1)^n.
%F A191497 From _R. J. Mathar_, Jun 23 2011: (Start)
%F A191497 G.f.: -x^4 / ((2*x-1)*(x^4+1)).
%F A191497 a(n) = (2^n - (-1)^floor(n/4)*A133145(n))/17. (End)
%p A191497 A191497 := proc(n): if n=0 then 0 else A191497(n) := 2*A191497(n-1) + A014017(n+4) fi: end: A014017 := proc(n): (1/8)*(-(n mod 8)-((n+3) mod 8)+((n+4) mod 8)+((n+7) mod 8)) end: seq(A191497(n),n=0..32); # _Johannes W. Meijer_, Jun 28 2011
%t A191497 LinearRecurrence[{2,0,0,-1,2},{0,0,0,0,1},40] (* _Harvey P. Dale_, Apr 19 2013 *)
%Y A191497 Cf. A014017, A133145.
%K A191497 nonn,easy
%O A191497 0,6
%A A191497 _Paul Curtz_, Jun 03 2011