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

Author

Sture Sjöstedt, May 31 2009

Keywords

• nonn
• easy

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).

Programs

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 *)

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

Extensions

Edited by N. J. A. Sloane, Jun 07 2009

Extended by Emeric Deutsch and R. J. Mathar, Jun 22 2009