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 A135032 a(n) = 6*a(n-1) + 4*a(n-2). 7
 0, 1, 6, 40, 264, 1744, 11520, 76096, 502656, 3320320, 21932544, 144876544, 956989440, 6321442816, 41756614656, 275825459200, 1821979213824, 12035177119744, 79498979573760, 525134585921536, 3468803433824256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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). 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 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 *) PROG (Sage) [lucas_number1(n, 6, -4) for n in xrange(0, 21)] # Zerinvary Lajos, Apr 24 2009 (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 (PARI) x='x+O('x^30); concat([0], Vec(x/(1-6*x-4*x^2))) \\ G. C. Greubel, Jan 24 2018 CROSSREFS Sequence in context: A026077 A065113 A052518 * A122074 A289208 A244253 Adjacent sequences:  A135029 A135030 A135031 * A135033 A135034 A135035 KEYWORD nonn,easy AUTHOR Rolf Pleisch, Feb 10 2008, corrected Feb 14 2008 EXTENSIONS More terms from Alexis Olson (AlexisOlson(AT)gmail.com), Nov 15 2008 STATUS approved

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Last modified October 20 08:05 EDT 2019. Contains 328252 sequences. (Running on oeis4.)