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

Author

Paul Barry, May 19 2003

Keywords

• easy
• nonn

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).

Programs

Magma

[(5*2^n-6*0^n+4*(-1)^n-3*(-2)^n)/12: n in [0..40]]; // Vincenzo Librandi, Aug 13 2011

Mathematica

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

PARI

a(n)=if(n,(5*2^n+4*(-1)^n-3*(-2)^n)/12,0) \\ Charles R Greathouse IV, Oct 24 2014

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