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A015533
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a(n) = 4*a(n-1) + 9*a(n-2).
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13
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0, 1, 4, 25, 136, 769, 4300, 24121, 135184, 757825, 4247956, 23812249, 133480600, 748232641, 4194255964, 23511117625, 131792774176, 738771155329, 4141219588900, 23213818753561, 130126251314344, 729429374039425, 4088853757986796, 22920279398302009
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OFFSET
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0,3
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COMMENTS
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For n>=2, a(n) equals the permanent of the (n-1) X (n-1) tridiagonal matrix with 4's along the main diagonal, and 3's along the superdiagonal and the subdiagonal. - John M. Campbell, Jul 19 2011
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LINKS
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FORMULA
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O.g.f.: x/(1-4*x-9*x^2).
a(n) = -9^n*(A^n - B^n)/(2*sqrt(13)) where A = -1/(2+sqrt(13)) and B = 1/(sqrt(13)-2). (End)
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MATHEMATICA
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a[n_]:=(MatrixPower[{{1, 4}, {1, -5}}, n].{{1}, {1}})[[2, 1]]; Table[Abs[a[n]], {n, -1, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)
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PROG
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(Sage) [lucas_number1(n, 4, -9) for n in range(0, 22)] # Zerinvary Lajos, Apr 23 2009
(Magma) [n le 2 select n-1 else 4*Self(n-1)+9*Self(n-2): n in [1..30] ]; // Vincenzo Librandi, Nov 12 2012
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-4*x-9*x^2))) \\ G. C. Greubel, Jan 01 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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