A101676 a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) with initial terms 1,0,-2,-1,0.
1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1).
Programs
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Magma
I:=[1, 0, -2, -1, 0]; [n le 5 select I[n] else Self(n-1) - Self(n-2) +Self(n-3) -Self(n-4) +Self(n-5): n in [1..100]]; // G. C. Greubel, Sep 07 2018
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Mathematica
LinearRecurrence[{1, -1, 1, -1, 1},{1, 0, -2, -1, 0},105] (* Ray Chandler, Sep 03 2015 *) -
PARI
x='x+O('x^100); Vec((1-x-x^2)/((1-x)*(1+x^2+x^4))) \\ G. C. Greubel, Sep 07 2018
Formula
G.f.: (1 - x - x^2)/((1 - x)*(1 + x^2 + x^4)).
a(n) = -cos(2*Pi*n/3+Pi/3)/3 + sin(2*Pi*n/3+Pi/3)/sqrt(3) + 2*cos(Pi*n/3+Pi/6)/sqrt(3) - 1/3.
Comments