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A015544
Lucas sequence U(5,-8): a(n+1) = 5*a(n) + 8*a(n-1), a(0)=0, a(1)=1.
3
0, 1, 5, 33, 205, 1289, 8085, 50737, 318365, 1997721, 12535525, 78659393, 493581165, 3097180969, 19434554165, 121950218577, 765227526205, 4801739379641, 30130517107845, 189066500576353, 1186376639744525, 7444415203333449, 46713089134623445
OFFSET
0,3
FORMULA
a(n) = 5*a(n-1) + 8*a(n-2).
G.f.: x/(1 - 5*x - 8*x^2). - M. F. Hasler, Mar 06 2009
MATHEMATICA
a[n_]:=(MatrixPower[{{1, 2}, {1, -6}}, n].{{1}, {1}})[[2, 1]]; Table[Abs[a[n]], {n, -1, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)
LinearRecurrence[{5, 8}, {0, 1}, 30] (* Vincenzo Librandi, Nov 13 2012 *)
PROG
(PARI) A015544(n)=imag((2+quadgen(57))^n) \\ M. F. Hasler, Mar 06 2009
(Sage) [lucas_number1(n, 5, -8) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009
(Magma) [n le 2 select n-1 else 5*Self(n-1) + 8*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 13 2012
(PARI) x='x+O('x^30); concat([0], Vec(x/(1 - 5*x - 8*x^2))) \\ G. C. Greubel, Jan 01 2018
KEYWORD
nonn,easy
EXTENSIONS
More precise definition by M. F. Hasler, Mar 06 2009
STATUS
approved