A191497 a(n+1) = 2*a(n) + A014017(n+5), a(0) = 0.
0, 0, 0, 0, 1, 2, 4, 8, 15, 30, 60, 120, 241, 482, 964, 1928, 3855, 7710, 15420, 30840, 61681, 123362, 246724, 493448, 986895, 1973790, 3947580, 7895160, 15790321, 31580642, 63161284, 126322568, 252645135
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (2,0,0,-1,2).
Programs
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Maple
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
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Mathematica
LinearRecurrence[{2,0,0,-1,2},{0,0,0,0,1},40] (* Harvey P. Dale, Apr 19 2013 *)
Formula
a(n+4) = 2^n - a(n).
a(n) = 2*a(n-1) - a(n-4) + 2*a(n-5).
a(4*n+4) = 16*a(4*n) + (-1)^n.
From R. J. Mathar, Jun 23 2011: (Start)
G.f.: -x^4 / ((2*x-1)*(x^4+1)).
a(n) = (2^n - (-1)^floor(n/4)*A133145(n))/17. (End)