A077980 Expansion of 1/(1 + x + 2*x^2 + 2*x^3).
1, -1, -1, 1, 3, -3, -5, 5, 11, -11, -21, 21, 43, -43, -85, 85, 171, -171, -341, 341, 683, -683, -1365, 1365, 2731, -2731, -5461, 5461, 10923, -10923, -21845, 21845, 43691, -43691, -87381, 87381, 174763, -174763, -349525, 349525, 699051, -699051, -1398101, 1398101, 2796203, -2796203, -5592405
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (-1,-2,-2).
Programs
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GAP
a:=[1,-1,-1];; for n in [4..50] do a[n]:=-a[n-1]-2*a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Jun 25 2019
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Magma
I:=[1,-1,-1]; [n le 3 select I[n] else -Self(n-1)-2*Self(n-2) -2*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Aug 17 2013
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Mathematica
LinearRecurrence[{-1, -2, -2}, {1, -1, -1}, 50] (* Vincenzo Librandi, Aug 17 2013 *) -
PARI
Vec(1/(1+x+2*x^2+2*x^3)+O(x^50)) \\ Charles R Greathouse IV, Sep 27 2012
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PARI
a(n)=1/3*(-1)^floor((n+1)/2)*((2^floor(n/2+1)+(-1)^floor(n/2))) \\ Ralf Stephan, Aug 17 2013
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Sage
(1/(1+x+2*x^2+2*x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 25 2019
Formula
a(n) = (1/3) * (-1)^floor((n+1)/2) * ((2^floor(n/2+1) + (-1)^floor(n/2))). - Ralf Stephan, Aug 17 2013
Comments