A141355 The Jacobsthal sequence, dropping each third term.

1, 1, 5, 11, 43, 85, 341, 683, 2731, 5461, 21845, 43691, 174763, 349525, 1398101, 2796203, 11184811, 22369621, 89478485, 178956971, 715827883, 1431655765, 5726623061, 11453246123, 45812984491, 91625968981, 366503875925, 733007751851

Offset: 0

Author

Paul Curtz, Aug 03 2008

Keywords

• nonn
• easy

Comments

A001045 after removal of the subsequence A132805.

Programs

Python

def A141355(n): return ((1<<(n+1<<1)-(n+1>>1)-1)|1)//3 # Chai Wah Wu, Apr 19 2025

Formula

a(2n+1)-a(2n) = 6*A015565(n).

a(4n+1)=2a(4n)-1. a(4n+2)=4a(4n+1)+1. a(4n+3)=2a(4n+2)+1. a(4n+4)=4a(4n+3)-1.

a(2n)= A082311(n). a(2n+1) = A082365(n). - R. J. Mathar, Feb 23 2009

a(n)=7*a(n-2)+8*a(n-4). G.f.: (1+x-2*x^2+4*x^3)/((1-8*x^2)*(1+x^2)). - R. J. Mathar, Feb 23 2009

Extensions

Edited and extended by R. J. Mathar, Feb 23 2009