A084241 a(n) = -5*a(n-1)-4*a(n-2) with n>1, a(0)=0, a(1)=1.

0, 1, -5, 21, -85, 341, -1365, 5461, -21845, 87381, -349525, 1398101, -5592405, 22369621, -89478485, 357913941, -1431655765, 5726623061, -22906492245, 91625968981, -366503875925, 1466015503701, -5864062014805, 23456248059221, -93824992236885

Offset: 0

Author

Paul Barry, May 21 2003

Keywords

• sign
• easy

Comments

Binomial transform is (0,1,-3,9,-27,...).

Links

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

Crossrefs

Apart from signs, identical to A002450.

Cf. A084240.

Programs

Mathematica

LinearRecurrence[{-5,-4},{0,1},40] (* Harvey P. Dale, Dec 20 2014 *)

Formula

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

a(n) = Sum_{k=1..n} (-1)^(n+k)*binomial(n, k)*(-3)^(k-1).

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

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

abs(a(n)) = A002450(n) = A001045(2n).