A160958 a(n) = (9^n - (-7)^n)/(9 - (-7)).

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.

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

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

Adjacent sequences: A160955 A160956 A160957 * A160959 A160960 A160961

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