OFFSET
1,2
COMMENTS
Theon from Smyrna used a(n+1)=2a(n)+a(n-1), a(1)=1, a(2)=2, to determine sqrt(2).
F(n) = (r^n - s^n)/(r - s) where r is different from s will generate Fibonacci-type sequences.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2,63).
FORMULA
a(n) = 2a(n-1)+63a(n-2), a(1)=1 a(2)=2.
G.f.: x/((1-9x)(1+7x)). - R. J. Mathar, Jun 22 2009
a(n+1) = Sum_{k = 0..n} A238801(n,k)*8^k. - Philippe Deléham, Mar 07 2014
MAPLE
a := proc (n) options operator, arrow: (1/16)*9^n-(1/16)*(-7)^n end proc: seq(a(n), n = 1 .. 20); # Emeric Deutsch, Jun 21 2009
MATHEMATICA
Table[(9^n - (-7)^n)/(9 - (-7)), {n, 20}] (* Wesley Ivan Hurt, Mar 07 2014 *)
CoefficientList[Series[1/((1 - 9 x) (1 + 7 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Mar 08 2014 *)
LinearRecurrence[{2, 63}, {1, 2}, 20] (* Harvey P. Dale, Aug 29 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sture Sjöstedt, May 31 2009
EXTENSIONS
Edited by N. J. A. Sloane, Jun 07 2009
Extended by Emeric Deutsch and R. J. Mathar, Jun 22 2009
STATUS
approved