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A084240
a(n) = -5*a(n-1) - 4*a(n-2), a(0)=1, a(1)=0.
3
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
0,3
COMMENTS
A Jacobsthal related sequence.
Inverse binomial transform of A084246.
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
MATHEMATICA
LinearRecurrence[{-5, -4}, {1, 0}, 30] (* Harvey P. Dale, Dec 13 2021 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, May 23 2003
STATUS
approved