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

%I

%S 0,1,-5,21,-85,341,-1365,5461,-21845,87381,-349525,1398101,-5592405,

%T 22369621,-89478485,357913941,-1431655765,5726623061,-22906492245,

%U 91625968981,-366503875925,1466015503701,-5864062014805,23456248059221,-93824992236885

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

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

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

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (-5,-4).

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

%F a(n) = sum(k=1..n, (-1)^(n+k)*binomial(n, k)(-3)^(k-1)).

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

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

%t LinearRecurrence[{-5,-4},{0,1},40] (* _Harvey P. Dale_, Dec 20 2014 *)

%Y Apart from signs, identical to A002450.

%Y Cf. A084240.

%K sign,easy

%O 0,3

%A _Paul Barry_, May 21 2003

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Last modified November 28 13:47 EST 2021. Contains 349413 sequences. (Running on oeis4.)