A166036 a(n) = (4^n+8*(-5)^n)/9.

1, -4, 24, -104, 584, -2664, 14344, -67624, 354504, -1706984, 8797064, -42936744, 218878024, -1077612904, 5455173384, -27007431464, 136110899144, -676259528424, 3398477511304, -16923668079784

Offset: 0

Author

Philippe Deléham, Oct 05 2009

Keywords

• easy
• sign

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,20).

Crossrefs

Cf. A077925, A091004, A166035.

Programs

Mathematica

Table[(4^n+8(-5)^n)/9,{n,0,30}] (* or *) LinearRecurrence[{-1,20},{1,-4},30] (* Harvey P. Dale, Mar 05 2016 *)

PARI

vector(100, n, n--; (4^n+8*(-5)^n)/9) \\ Altug Alkan, Apr 24 2016

Formula

a(n) = -a(n-1) + 20*a(n-2), a(0) = 1, a(1) = -4, for n>1.

a(n) = Sum_{k=0..n} A112555(n,k)*(-5)^k.

G.f.: (1-3x)/(1+x-20x^2).

E.g.f.: (1/9)*(exp(4*x) + 8*exp(-5*x)). - G. C. Greubel, Apr 24 2016