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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 (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 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

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Last modified September 9 04:58 EDT 2024. Contains 375759 sequences. (Running on oeis4.)