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a(n) = 9*a(n-1) + 6*a(n-2); a(0)=0, a(1)=1.
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%I #30 Jan 03 2024 08:46:28

%S 0,1,9,87,837,8055,77517,745983,7178949,69086439,664851645,6398183439,

%T 61572760821,592543948023,5702332097133,54876252562335,

%U 528100265643813,5082159906168327,48908040749377821,470665326181410351

%N a(n) = 9*a(n-1) + 6*a(n-2); a(0)=0, a(1)=1.

%H G. C. Greubel, <a href="/A153191/b153191.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 (9, 6).

%F G.f.: x/(1 - 9*x - 6*x^2).

%p a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=9*a[n-1]+6*a[n-2]od: seq(a[n], n=0..33);

%t LinearRecurrence[{9,6}, {0,1}, 25] (* _G. C. Greubel_, Jan 24 2018 *)

%o (Sage) [lucas_number1(n,9,-6) for n in range(0, 25)]# _Zerinvary Lajos_, Apr 26 2009

%o (PARI) x='x+O('x^25); concat([0], Vec(x/(1-9*x-6*x^2))) \\ _G. C. Greubel_, Jan 24 2018

%o (Magma) I:=[0,1]; [n le 2 select I[n] else 9*Self(n-1) + 6*Self(n-2): n in [1..25]]; // _G. C. Greubel_, Jan 24 2018

%Y Cf. A015579, A099371.

%K nonn

%O 0,3

%A _Zerinvary Lajos_, Dec 20 2008

%E Formula corrected by _Philippe Deléham_, Dec 20 2008

%E Edited by _N. J. A. Sloane_, Dec 21 2008