A106603 a(n) = - 2*a(n-1) - 8*a(n-3), a(0) = 1, a(1) = 1, a(2) = -2.
1, 1, -2, -4, 0, 16, 0, 0, -128, 256, -512, 2048, -6144, 16384, -49152, 147456, -425984, 1245184, -3670016, 10747904, -31457280, 92274688, -270532608, 792723456, -2323644416, 6811549696, -19964887040, 58518929408, -171530256384, 502779609088, -1473710653440, 4319663357952
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (-2,0,-8).
Programs
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Magma
I:=[1,1,-2]; [n le 3 select I[n] else (-2)*(Self(n-1) +4*Self(n-3)): n in [1..41]]; // G. C. Greubel, Sep 08 2021
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Mathematica
LinearRecurrence[{-2,0,-8}, {1,1,-2}, 41] (* G. C. Greubel, Sep 08 2021 *)
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SageMath
def A106603_list(prec): P.
= PowerSeriesRing(ZZ, prec) return P( (1+3*x)/(1+2*x+8*x^3) ).list() A106603_list(40) # G. C. Greubel, Sep 08 2021
Formula
G.f.: (1 + 3*x)/(1 + 2*x + 8*x^3).
a(n) = b(n) + 3*b(n-1), where b(n) = 2^n*A199804(n). - R. J. Mathar, Sep 11 2019
a(n) = (-2)^(n-1)*(-2*c(n) + 3*c(n-1)), where c(n) = A000930(n). - G. C. Greubel, Sep 08 2021
Comments