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%I #15 Feb 24 2019 01:36:15
%S 0,0,0,0,1,2,4,8,15,30,60,120,241,482,964,1928,3855,7710,15420,30840,
%T 61681,123362,246724,493448,986895,1973790,3947580,7895160,15790321,
%U 31580642,63161284,126322568,252645135
%N a(n+1) = 2*a(n) + A014017(n+5), a(0) = 0.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,-1,2).
%F a(n+4) = 2^n - a(n).
%F a(n) = 2*a(n-1) - a(n-4) + 2*a(n-5).
%F a(4*n+4) = 16*a(4*n) + (-1)^n.
%F G.f.: -x^4 / ((2*x-1)*(x^4+1)). - _R. J. Mathar_, Jun 23 2011
%F a(n) = (2^n - (-1)^floor(n/4)*A133145(n))/17. - _R. J. Mathar_, Jun 23 2011
%p 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 LinearRecurrence[{2,0,0,-1,2},{0,0,0,0,1},40] (* _Harvey P. Dale_, Apr 19 2013 *)
%K nonn,easy
%O 0,6
%A _Paul Curtz_, Jun 03 2011
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