A084183 Jacobsthal reverse-pair sequence.

0, 1, 1, 5, 3, 21, 11, 85, 43, 341, 171, 1365, 683, 5461, 2731, 21845, 10923, 87381, 43691, 349525, 174763, 1398101, 699051, 5592405, 2796203, 22369621, 11184811, 89478485, 44739243, 357913941, 178956971, 1431655765, 715827883, 5726623061

Offset

0,4

Comments

Reverses elements a(2n+1) and a(2n+2) in A001045.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1,4,4).

Formula

G.f.: x*(1 + 2*x + 2*x^2)/((1+x)(1+2x)(1-2x)).

a(n) = (5*2^n - 6*0^n + 4(-1)^n - 3(-2)^n)/12. - Paul Barry, May 19 2003

a(n) - 2*a(n-1) is a signed version of A000225. - Paul Curtz, Mar 06 2008

Mathematica

LinearRecurrence[{-1, 4, 4}, {0, 1, 1, 5}, 40] (* Harvey P. Dale, Nov 26 2022 *)

Prog

(Magma) [(5*2^n-6*0^n+4*(-1)^n-3*(-2)^n)/12: n in [0..40]]; // Vincenzo Librandi, Aug 13 2011
(PARI) a(n)=if(n, (5*2^n+4*(-1)^n-3*(-2)^n)/12, 0) \\ Charles R Greathouse IV, Oct 24 2014

Crossrefs

Sequence in context: A070262 A372289 A171621 * A099730 A072800 A199637

Adjacent sequences: A084180 A084181 A084182 * A084184 A084185 A084186

Keyword

easy,nonn

Author

Paul Barry, May 19 2003

Status

approved