OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,8).
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
CROSSREFS
Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015537, A015441, A015443, A015447, A030195, A053404, A057087, A057088, A083858, A085939, A090017, A091914, A099012, A180222, A180226, A015555 (binom. transf.).
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More precise definition by M. F. Hasler, Mar 06 2009
STATUS
approved