OFFSET
0,1
COMMENTS
LINKS
Wikipedia, Lucas sequence: Specific names.
Index entries for linear recurrences with constant coefficients, signature (3,3).
FORMULA
L(k,n) = c^n+b^n where c=(k+d)/2 ; b=(k-d)/2; d=sqrt(k*(k+4)) (Binet formula).
a(0)=2, a(1)=3, a(n) = 3*a(n-1)+3*a(n-2). [Harvey P. Dale, Aug 24 2011]
a(n) = [x^n] ( (1 + 3*x + sqrt(1 + 6*x + 21*x^2))/2 )^n for n >= 1. - Peter Bala, Jun 23 2015
MATHEMATICA
CoefficientList[Series[(2-3x)/(1-3x-3x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, 3}, {2, 3}, 31] (* Harvey P. Dale, Aug 24 2011 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Claudio Peruzzi (claudio.peruzzi(AT)gmail.com), Jan 22 2010
EXTENSIONS
Edited and extended by R. J. Mathar, Jan 23 2010
STATUS
approved