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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
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.
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
A160958 := proc(n) (9^n-(-7)^n)/16 ; end: seq(A160958(n), n=1..30) ; # R. J. Mathar, Jun 22 2009
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
Sequence in context: A371509 A174602 A154880 * A046848 A318064 A089661
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