OFFSET
1,1
COMMENTS
20 of the first 100 terms are prime numbers.
LINKS
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (1,1).
FORMULA
G.f.: (12*x+55*x^2)/(1-x-x^2). - Philippe Deléham, Nov 20 2008
a(n) = (61*sqrt(5)/5 + 6)*(1/2 + sqrt(5)/2)^n + (-61*sqrt(5)/5 + 6)*(1/2 - sqrt(5)/2)^n. - Antonio Alberto Olivares, May 23 2013
EXAMPLE
a(0) = (61*sqrt(5)/5 + 6)*(1/2 + sqrt(5)/2)^0 + (-61*sqrt(5)/5 + 6)*(1/2 - sqrt(5)/2)^0 =(61*sqrt(5)/5 + 6) + (-61*sqrt(5)/5 + 6) = 6 + 6 = 12.
MATHEMATICA
a={}; b=12; c=67; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 12, 1}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)
LinearRecurrence[{1, 1}, {12, 67}, 50] (* or *) Rest[ CoefficientList[ Series[ (12x+55x^2)/(1-x-x^2), {x, 0, 50}], x]] (* Harvey P. Dale, May 11 2011 *)
PROG
(Magma) a0:=12; a1:=67; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..35]]; // Vincenzo Librandi, Nov 02 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
G. L. Honaker, Jr., Dec 17 2003
STATUS
approved