A141354 Expansion of (1-5*x-x^2+x^3)/((1+x)*(1-x)^3).
1, -3, -7, -15, -23, -35, -47, -63, -79, -99, -119, -143, -167, -195, -223, -255, -287, -323, -359, -399, -439, -483, -527, -575, -623, -675, -727, -783, -839, -899, -959, -1023, -1087, -1155, -1223, -1295, -1367, -1443, -1519, -1599, -1679, -1763, -1847
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
Programs
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Magma
[((-1)^n-2*n^2-4*n+1)/2 : n in [0..100]]; // Wesley Ivan Hurt, Sep 08 2015
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Magma
I:=[1,-3,-7,-15]; [n le 4 select I[n] else 2*Self(n-1)-2*Self(n-3)+Self(n-4): n in [1..50]]; // Vincenzo Librandi, Sep 10 2015
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Maple
A141354:=n->((-1)^n-2*n^2-4*n+1)/2: seq(A141354(n), n=0..100); # Wesley Ivan Hurt, Sep 08 2015
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Mathematica
CoefficientList[Series[(1-5x-x^2+x^3)/((1+x)(1-x)^3),{x,0,42}],x] (* Ray Chandler, Dec 05 2011 *) LinearRecurrence[{2, 0, -2, 1}, {1, -3, -7, -15}, 60] (* Vincenzo Librandi, Sep 10 2015 *)
Formula
G.f.: (1-5*x-x^2+x^3)/(1-2*x+2*x^3-x^4).
a(n) = -A181106(n+1).
From Wesley Ivan Hurt, Sep 08 2015: (Start)
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4), n>3.
a(n) = ((-1)^n-2*n^2-4*n+1)/2. (End)
Extensions
Edited by Ray Chandler, Dec 05 2011
Comments