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a(n) = 4*a(n-1) + 4*a(n-2) - a(n-3); a(0)=1, a(1)=1, a(2)=7.
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%I #17 Jan 01 2024 11:48:03

%S 1,1,7,31,151,721,3457,16561,79351,380191,1821607,8727841,41817601,

%T 200360161,959983207,4599555871,22037796151,105589424881,505909328257,

%U 2423957216401,11613876753751,55645426552351,266613256008007

%N a(n) = 4*a(n-1) + 4*a(n-2) - a(n-3); a(0)=1, a(1)=1, a(2)=7.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,4,-1).

%F a(n) = 5*a(n-1)-a(n-2)+3*(-1)^n.

%F G.f.: (1-3*x-x^2)/(1-4*x-4*x^2+x^3).

%t LinearRecurrence[{4,4,-1},{1,1,7},30] (* _Harvey P. Dale_, Jan 28 2020 *)

%t CoefficientList[Series[(1-3*x-x^2)/(1-4*x-4*x^2+x^3),{x,0,30}],x] (* _Harvey P. Dale_, Jun 20 2021 *)

%K nonn,easy

%O 0,3

%A _Philippe Deléham_, Sep 08 2006