A206372 a(n) = 14 * 4^n - 1.
13, 55, 223, 895, 3583, 14335, 57343, 229375, 917503, 3670015, 14680063, 58720255, 234881023, 939524095, 3758096383, 15032385535, 60129542143, 240518168575, 962072674303, 3848290697215, 15393162788863, 61572651155455, 246290604621823, 985162418487295
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5, -4).
Programs
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Magma
[14*4^n-1 : n in [0..30]];
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Mathematica
7*2^(2*Range[0,50]+1)-1 (* G. C. Greubel, Jan 05 2023 *)
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PARI
a(n)=14*4^n - 1 \\ Charles R Greathouse IV, May 05 2014
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SageMath
[7*2^(2*n+1)-1 for n in range(51)] # G. C. Greubel, Jan 05 2023
Formula
a(n) = 7*2^(2*n+1) - 1.
a(n) = (A199207(n+1) -3)/2 for n>=0.
From G. C. Greubel, Jan 05 2023: (Start)
a(n) = A005009(2*n+1) - 1.
G.f.: (13 - 10*x)/((1-x)*(1-4*x)).
E.g.f.: 14*exp(4*x) - exp(x). (End)