A135032 a(n) = 6*a(n-1) + 4*a(n-2).

0, 1, 6, 40, 264, 1744, 11520, 76096, 502656, 3320320, 21932544, 144876544, 956989440, 6321442816, 41756614656, 275825459200, 1821979213824, 12035177119744, 79498979573760, 525134585921536, 3468803433824256

Offset: 0

Author

Rolf Pleisch, Feb 10 2008, corrected Feb 14 2008

Keywords

• nonn
• easy

Comments

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,4).

Programs

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

Mathematica

Join[{a=0,b=1},Table[c=6*b+4*a;a=b;b=c,{n,100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)
LinearRecurrence[{6,4}, {0,1}, 25] (* G. C. Greubel, Sep 17 2016 *)

PARI

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

Sage

[lucas_number1(n,6,-4) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009

Formula

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

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

from R. J. Mathar, Oct 15 2012: (Start)

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

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

E.g.f.: (1/sqrt(13))*exp(3*x)*sinh(sqrt(13)*x). - G. C. Greubel, Sep 17 2016

Extensions

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