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a(n)=-a(n-1)+3*a(n-2), n>1 ; a(0)=1, a(1)=-3 .
4

%I #19 Apr 09 2024 08:09:06

%S 1,-3,6,-15,33,-78,177,-411,942,-2175,5001,-11526,26529,-61107,140694,

%T -324015,746097,-1718142,3956433,-9110859,20980158,-48312735,

%U 111253209,-256191414,589951041,-1358525283,3128378406,-7203954255,16589089473

%N a(n)=-a(n-1)+3*a(n-2), n>1 ; a(0)=1, a(1)=-3 .

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,3).

%F G.f.: (1-2*x)/(1+x-3*x^2).

%F a(n) = (-1)^n*A105476(n+1).

%F a(n) = Sum{k=0..n} A147703(n,k)*(-4)^k.

%t LinearRecurrence[{-1,3},{1,-3},30] (* _Harvey P. Dale_, Dec 24 2013 *)

%o (PARI) Vec((1-2*x)/(1+x-3*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Jan 11 2012

%Y Cf. A105476, A147703.

%K sign,easy

%O 0,2

%A _Philippe Deléham_, Nov 27 2008

%E a(19) corrected by _Charles R Greathouse IV_, Jan 11 2012