A165748 a(n) = (8/9)*(2+7*(-8)^(n-1)).

1, 8, -48, 400, -3184, 25488, -203888, 1631120, -13048944, 104391568, -835132528, 6681060240, -53448481904, 427587855248, -3420702841968, 27365622735760, -218924981886064, 1751399855088528, -14011198840708208

Offset: 0

Author

Philippe Deléham, Sep 26 2009

Keywords

• easy
• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (-7,8).

Programs

Mathematica

Table[(8/9)*(2 + 7*(-8)^(n - 1)), {n, 0, 100}] or
LinearRecurrence[{-7,8}, {1,8}, 100] (* G. C. Greubel, Apr 07 2016 *)

PARI

x='x+O('x^99); Vec((1+15*x)/(1+7*x-8*x^2)) \\ Altug Alkan, Apr 07 2016

Formula

a(n) = (-8)*a(n-1) + 16 for n>=1, with a(0) = 1.

a(n) = 8*a(n-2) - 7*a(n-1), a(0)=1, a(1)=8.

G.f.: (1+15x)/(1+7x-8x^2).

a(n) = Sum_{0<=k<=n} A112555(n,k)*7^(n-k).

From G. C. Greubel, Apr 07 2016: (Start)

a(n) = -7*a(n-1) + 8*a(n-2).

E.g.f.: (1/9)*(16*exp(x) - 7*exp(-8*x)). (End)