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

0,3

Comments

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

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

Links

Table of n, a(n) for n=0..24.

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

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.

Mathematica

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

Crossrefs

Apart from signs, identical to A002450.

Cf. A084240.

Sequence in context: A271157 A255451 A028948 * A002450 A187063 A026855

Adjacent sequences: A084238 A084239 A084240 * A084242 A084243 A084244

Keyword

sign,easy

Author

Paul Barry, May 21 2003

Status

approved