A032127 "BIK" (reversible, indistinct, unlabeled) transform of 1,3,5,7...

1, 4, 9, 25, 63, 183, 513, 1521, 4455, 13311, 39609, 118665, 355023, 1064583, 3190833, 9571041, 28704375, 86108751, 258300009, 774886905, 2324581983, 6973706583, 20920883553, 62762532561, 188286889095, 564860312991, 1694578813209, 5083735376745, 15251199752943

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

C. G. Bower, Transforms (2)

Index entries for linear recurrences with constant coefficients, signature (3,3,-9).

Formula

For n>2, a(n) = (1/9)*((8-(-1)^n)*3^floor(n/2) + 2*3^n). - Ralf Stephan, May 11 2004

G.f.: -x*(3*x^4+5*x^3+6*x^2-x-1) / ((3*x-1)*(3*x^2-1)). - Colin Barker, Dec 15 2012

Mathematica

CoefficientList[Series[-(3 x^4 + 5 x^3 + 6 x^2 - x - 1)/((3 x - 1) (3 x^2 - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 19 2013 *)
LinearRecurrence[{3, 3, -9}, {1, 4, 9, 25, 63}, 30] (* Harvey P. Dale, Feb 20 2016 *)

Prog

(Magma) [1, 4] cat [(1/9)*((8-(-1)^n)*3^Floor(n/2) + 2*3^n): n in [3..30]]; // Vincenzo Librandi, Oct 19 2013

Crossrefs

Sequence in context: A030481 A160190 A226917 * A181357 A244558 A175627

Adjacent sequences: A032124 A032125 A032126 * A032128 A032129 A032130

Keyword

nonn,easy

Author

Christian G. Bower

Extensions

More terms from Vincenzo Librandi, Oct 19 2013

Status

approved