A107584 a(n) = 4^n - 4*n.
1, 0, 8, 52, 240, 1004, 4072, 16356, 65504, 262108, 1048536, 4194260, 16777168, 67108812, 268435400, 1073741764, 4294967232, 17179869116, 68719476664, 274877906868, 1099511627696, 4398046511020, 17592186044328, 70368744177572, 281474976710560, 1125899906842524
Offset: 0
Examples
Corresponding numbers m are 1, 4, 1111111144, ...
Links
- Index entries for linear recurrences with constant coefficients, signature (6,-9,4).
Programs
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Magma
[(4^n - 4*n): n in [0..25]]; // Vincenzo Librandi, Dec 16 2010
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Mathematica
Table[4^m-4*m, {m, 0, 20}] LinearRecurrence[{6,-9,4},{1,0,8},30] (* Harvey P. Dale, Oct 21 2011 *) -
PARI
a(n)=4^n-4*n \\ Charles R Greathouse IV, Sep 08 2012
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Python
def A107584(n): return (1<<(n<<1))-(n<<2) # Chai Wah Wu, Nov 29 2023
Formula
From Harvey P. Dale, Oct 21 2011: (Start)
a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3) with a(0)=1, a(1)=0, and a(2)=8.
G.f.: (-17*x^2+6*x-1)/((x-1)^2*(4*x-1)). (End)
E.g.f.: exp(x)*(exp(3*x) - 4*x). - Elmo R. Oliveira, Sep 10 2024
Extensions
More terms from Vincenzo Librandi, Dec 16 2010
Corrected by Charles R Greathouse IV, Sep 08 2012
Comments