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a(n) = 10*a(n-1) - a(n-2) for n >= 2 with a(0) = 1 and a(1) = 3.
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%I #16 Jan 02 2024 09:05:06

%S 1,3,29,287,2841,28123,278389,2755767,27279281,270037043,2673091149,

%T 26460874447,261935653321,2592895658763,25667020934309,

%U 254077313684327,2515106115908961,24896983845405283,246454732338143869,2439650339536033407,24150048663022190201

%N a(n) = 10*a(n-1) - a(n-2) for n >= 2 with a(0) = 1 and a(1) = 3.

%C a(n)/a(n-1) tends to 2*sqrt(6) + 5 = 9.8989794855...

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, -1).

%F Term (1,1) in A^n where A = the 2 X 2 matrix [3,4; 5,7].

%F G.f.: (1-7*x)/(x^2-10*x+1). - _Harvey P. Dale_, Jan 19 2012

%e a(3) = 287 = 10*a(2) - a(1) = 10*29 - 3.

%e a(3) = 287 = term (1,1) in A^3.

%t LinearRecurrence[{10,-1},{1,3},30] (* _Harvey P. Dale_, Jan 19 2012 *)

%K nonn

%O 0,2

%A _Gary W. Adamson_, May 30 2008

%E More terms from _Harvey P. Dale_, Jan 19 2012