A165755 a(n) = (5-3*5^n)/2.

1, -5, -35, -185, -935, -4685, -23435, -117185, -585935, -2929685, -14648435, -73242185, -366210935, -1831054685, -9155273435, -45776367185, -228881835935, -1144409179685, -5722045898435, -28610229492185

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 (6, -5).

Programs

Mathematica

(5-3*5^Range[0,20])/2 (* or *) LinearRecurrence[{6,-5},{1,-5},20] (* Harvey P. Dale, Apr 18 2013 *)

PARI

x='x+O('x^99); Vec((1-11*x)/(1-6*x+5*x^2)) \\ Altug Alkan, Apr 07 2016

Formula

a(n) = 5*a(n-1) - 10, a(0)=1.

a(n) = 6*a(n-1)-5*a(n-2), a(0)= 1, a(1)= -5, for n>1.

G.f.: (1-11x)/(1-6x+5x^2).

a(n) = Sum_{0<=k<=n} A112555(n,k)*(-6)^(n-k).

a(n) = (-5)*A057651(n-1).

E.g.f.: (1/2)*(5*exp(x) - 3*exp(5*x)). - G. C. Greubel, Apr 07 2016