A128416 Expansion of (1-4x^2)/(1+4x+3x^2).
1, -4, 9, -24, 69, -204, 609, -1824, 5469, -16404, 49209, -147624, 442869, -1328604, 3985809, -11957424, 35872269, -107616804, 322850409, -968551224, 2905653669, -8716961004, 26150883009, -78452649024, 235357947069, -706073841204, 2118221523609
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (-4,-3).
Crossrefs
Cf. A128414.
Programs
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PARI
Vec((1-4*x^2)/(1+4*x+3*x^2) + O(x^30)) \\ Colin Barker, Sep 21 2016
Formula
G.f.: (1-4*x^2)/(1+4*x+3*x^2).
For n > 1, |a(n)| = 3*(|a(n-1)| - 1). - Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Sep 17 2010
From Colin Barker, Sep 21 2016: (Start)
a(n) = (-1)^n*(9+5*3^n)/6 for n>0.
a(n) = -4*a(n-1)-3*a(n-2) for n>2. (End)
Comments