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a(0)=1, a(1)=5, a(n) = -3*a(n-1), n>1.
5

%I #19 Mar 20 2023 21:07:05

%S 1,5,-15,45,-135,405,-1215,3645,-10935,32805,-98415,295245,-885735,

%T 2657205,-7971615,23914845,-71744535,215233605,-645700815,1937102445,

%U -5811307335,17433922005,-52301766015,156905298045,-470715894135,1412147682405,-4236443047215

%N a(0)=1, a(1)=5, a(n) = -3*a(n-1), n>1.

%C Binomial transform is A083581.

%H Winston de Greef, <a href="/A084244/b084244.txt">Table of n, a(n) for n = 0..2081</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (-3).

%F a(n) = 8*0^n/3 - 5*(-3)^n/3.

%F G.f.: (1 + 8*x)/(1 + 3*x).

%F E.g.f.: (8 - 5*exp(-3*x))/3.

%t Join[{1},NestList[-3#&,5,30]] (* _Harvey P. Dale_, Jan 29 2013 *)

%o (PARI) a(n)=8*0^n/3 - 5*(-3)^n/3 \\ _Winston de Greef_, Mar 19 2023

%Y Cf. A083581.

%K easy,sign

%O 0,2

%A _Paul Barry_, May 23 2003