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a(n) = 14*a(n-1)-43*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
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%I #7 Sep 08 2022 08:45:47

%S 1,11,111,1081,10361,98571,934471,8844041,83634321,790586731,

%T 7471938431,70611908601,667273367881,6305515080491,59584456307991,

%U 563045239850761,5320501736667041,50276078999755851,475083531319899151

%N a(n) = 14*a(n-1)-43*a(n-2) for n > 1; a(0) = 1, a(1) = 11.

%C Binomial transform of A164552.

%H Harvey P. Dale, <a href="/A164553/b164553.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14, -43).

%F a(n) = ((3+2*sqrt(6))*(7+sqrt(6))^n+(3-2*sqrt(6))*(7-sqrt(6))^n)/6.

%F G.f.: (1-3*x)/(1-14*x+43*x^2).

%t LinearRecurrence[{14,-43},{1,11},30] (* _Harvey P. Dale_, Mar 10 2013 *)

%o (Magma) [ n le 2 select 10*n-9 else 14*Self(n-1)-43*Self(n-2): n in [1..19] ];

%Y Cf. A164552.

%K nonn

%O 0,2

%A _Klaus Brockhaus_, Aug 15 2009