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a(n) = 6*a(n-1) + 4*a(n-2).
7

%I #32 Sep 08 2022 08:45:32

%S 0,1,6,40,264,1744,11520,76096,502656,3320320,21932544,144876544,

%T 956989440,6321442816,41756614656,275825459200,1821979213824,

%U 12035177119744,79498979573760,525134585921536,3468803433824256

%N a(n) = 6*a(n-1) + 4*a(n-2).

%C For n>=2, a(n) equals the permanent of the (n-1)X(n-1) tridiagonal matrix with 6's along the main diagonal, and 2's along the superdiagonal and the subdiagonal. - _John M. Campbell_, Jul 19 2011

%H G. C. Greubel, <a href="/A135032/b135032.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 (6,4).

%F a(0)=0; a(1)=1; a(n) = 2*(3*a(n-1) + 2*a(n-2)).

%F a(n) = 1/(2*sqrt(13))*( (3 + sqrt(13))^n - (3 - sqrt(13))^n ).

%F from _R. J. Mathar_, Oct 15 2012: (Start)

%F a(n+1) = 2^n*A006190(n+1).

%F G.f.: x /( 1 - 6*x - 4*x^2 ). (End)

%F E.g.f.: (1/sqrt(13))*exp(3*x)*sinh(sqrt(13)*x). - _G. C. Greubel_, Sep 17 2016

%t Join[{a=0,b=1},Table[c=6*b+4*a;a=b;b=c,{n,100}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 16 2011 *)

%t LinearRecurrence[{6,4}, {0,1}, 25] (* _G. C. Greubel_, Sep 17 2016 *)

%o (Sage) [lucas_number1(n,6,-4) for n in range(0, 21)] # _Zerinvary Lajos_, Apr 24 2009

%o (Magma) [n le 2 select n-1 else 6*Self(n-1)+4*Self(n-2): n in [1..35]]; // _Vincenzo Librandi_, Sep 18 2016

%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-6*x-4*x^2))) \\ _G. C. Greubel_, Jan 24 2018

%K nonn,easy

%O 0,3

%A _Rolf Pleisch_, Feb 10 2008, corrected Feb 14 2008

%E More terms from Alexis Olson (AlexisOlson(AT)gmail.com), Nov 15 2008