A084240 a(n) = -5*a(n-1) - 4*a(n-2), a(0)=1, a(1)=0.

1, 0, -4, 20, -84, 340, -1364, 5460, -21844, 87380, -349524, 1398100, -5592404, 22369620, -89478484, 357913940, -1431655764, 5726623060, -22906492244, 91625968980, -366503875924, 1466015503700, -5864062014804, 23456248059220, -93824992236884, 375299968947540

Offset: 0

Author

Paul Barry, May 23 2003

Keywords

• easy
• sign

Comments

A Jacobsthal related sequence.

Inverse binomial transform of A084246.

Links

• Index entries for linear recurrences with constant coefficients, signature (-5,-4).

Crossrefs

Cf. A001045, A002450, A080674, A084241.

Programs

Mathematica

LinearRecurrence[{-5,-4},{1,0},30] (* Harvey P. Dale, Dec 13 2021 *)

Formula

G.f.: (1+5*x)/((1+x)*(1+4*x)).

E.g.f.: (4*exp(-x) - exp(-4*x))/3.

a(n) = A084241(n) + (-1)^n

a(n) = (-1)^(n+1)*(A002450(n)-1) = (-1)^(n+1)*(A001045(2*n)-1).

a(n) = (4*(-1)^n - (-4)^n)/3.

a(n) = (-1)^(n-1) * A080674(n-1). - Falk Hüffner, Jan 11 2021