A166114 a(n) = (6-(-4)^n)/5.
1, 2, -2, 14, -50, 206, -818, 3278, -13106, 52430, -209714, 838862, -3355442, 13421774, -53687090, 214748366, -858993458, 3435973838, -13743895346, 54975581390, -219902325554, 879609302222, -3518437208882, 14073748835534, -56294995342130
Offset: 0
Links
- Georg Fischer, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (-3,4).
Programs
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Mathematica
Table[(6 - (-4)^n)/5, {n, 0, 100}] (* G. C. Greubel, Apr 24 2016 *) -
PARI
a(n)=(6-(-4)^n)/5 \\ Charles R Greathouse IV, Apr 28 2016
Formula
a(n) = 4*a(n-2) - 3*a(n-1), a(0)= 1, a(1)= 2, for n>1.
a(n) = 6 - 4*a(n-1), a(0)=1.
a(n) = a(n-1) + (-4)^(n-1), a(0)=1.
G.f.: (1+5x)/(1+3x-4x^2).
E.g.f.: (6*exp(x) - exp(-4x))/5.
Extensions
a(12) onward changed by Georg Fischer, May 03 2019