|
|
A160958
|
|
a(n) = (9^n - (-7)^n)/(9 - (-7)).
|
|
2
|
|
|
1, 2, 67, 260, 4741, 25862, 350407, 2330120, 26735881, 200269322, 2084899147, 16786765580, 164922177421, 1387410586382, 13164918350287, 113736703642640, 1056863263353361, 9279138856193042, 85140663303647827, 754867074547457300
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
a(n) = 2a(n-1)+63a(n-2), a(1)=1 a(2)=2.
|
|
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
|
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
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|