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A032097 "BHK" (reversible, identity, unlabeled) transform of 2,1,1,1... 2
2, 2, 5, 14, 39, 107, 289, 772, 2047, 5402, 14213, 37325, 97905, 256622, 672337, 1760998, 4611643, 12075527, 31617521, 82781216, 216732891, 567428402, 1485570025, 3889310329, 10182407329, 26657986682, 69791674109, 182717232062, 478360339887 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 (5,-7,1,3,-1).

FORMULA

For n>1, a(n) = 1/2*[F(2n+1) - F(n+2) + 2], where F(n) = A000045(n). - Ralf Stephan, May 04 2004

G.f.: x*(x^5-4*x^4+x^3+9*x^2-8*x+2)/((x-1)*(x^2-3*x+1)*(x^2+x-1)). - Colin Barker, Sep 22 2012

MATHEMATICA

CoefficientList[Series[(x^5 - 4 x^4 + x^3 + 9 x^2 - 8 x + 2)/((x - 1) (x^2 - 3 x + 1) (x^2 + x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 19 2013 *)

PROG

(MAGMA) [2] cat [1/2*(Fibonacci(2*n+1) - Fibonacci(n+2) + 2): n in [2..30]]; // Vincenzo Librandi, Oct 19 2013

CROSSREFS

Sequence in context: A282275 A208201 A185966 * A176856 A112709 A291573

Adjacent sequences:  A032094 A032095 A032096 * A032098 A032099 A032100

KEYWORD

nonn,easy

AUTHOR

Christian G. Bower

EXTENSIONS

More terms from Vincenzo Librandi, Oct 19 2013

STATUS

approved

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Last modified February 21 06:25 EST 2018. Contains 299390 sequences. (Running on oeis4.)