A135094 a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3) with n>2, a(0)=0, a(1)=1, a(2)=3.
0, 1, 3, 8, 18, 40, 84, 176, 360, 736, 1488, 3008, 6048, 12160, 24384, 48896, 97920, 196096, 392448, 785408, 1571328, 3143680, 6288384, 12578816, 25159680, 50323456, 100651008, 201310208, 402628608, 805273600, 1610563584, 3221159936
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,2,-4).
Programs
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Magma
I:=[0,1,3]; [n le 3 select I[n] else 2*Self(n-1)+2*Self(n-2)-4*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Sep 23 2016
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Mathematica
LinearRecurrence[{2, 2, -4}, {0, 1, 3}, 50] (* G. C. Greubel, Sep 22 2016 *)
Formula
From R. J. Mathar, Feb 15 2008: (Start)
O.g.f.: -3/(2*(2*x-1)) + (4*x+3)/(2*(2*x^2-1)).
a(n) = 3*2^(n-1) - A063759(n+1)/2. (End)
From Colin Barker, Sep 23 2016: (Start)
a(n) = 3*2^(n-1) - 3*2^(n/2-1) for n even.
a(n) = 3*2^(n-1) - 2^((n+1)/2) for n odd. (End)
Extensions
More terms from R. J. Mathar, Feb 15 2008