OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,11).
FORMULA
a(n) = 3*a(n-1) + 11*a(n-2).
a(n) = -22^n*(A^n - B^n)/sqrt(53) where A = -1/(3+sqrt(53)) and B = 1/(sqrt(53)-3). - R. J. Mathar, Apr 29 2008
MATHEMATICA
Join[{a=0, b=1}, Table[c=3*b+11*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)
LinearRecurrence[{3, 11}, {0, 1}, 30] (* Vincenzo Librandi, Nov 12 2012 *)
CoefficientList[Series[x/(1-3x-11x^2), {x, 0, 30}], x] (* Harvey P. Dale, Aug 19 2024 *)
PROG
(Sage) [lucas_number1(n, 3, -11) for n in range(0, 22)] # Zerinvary Lajos, Apr 22 2009
(Magma) [n le 2 select n-1 else 3*Self(n-1) + 11*Self(n-2): n in [1..30] ]; // Vincenzo Librandi, Nov 12 2012
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-3*x-11*x^2))) \\ G. C. Greubel, Jan 01 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved