A092808 Pair reversal of Jacobsthal numbers.

1, 0, 3, 1, 11, 5, 43, 21, 171, 85, 683, 341, 2731, 1365, 10923, 5461, 43691, 21845, 174763, 87381, 699051, 349525, 2796203, 1398101, 11184811, 5592405, 44739243, 22369621, 178956971, 89478485, 715827883, 357913941, 2863311531, 1431655765

Offset: 0

Author

Paul Barry, Mar 10 2004

Keywords

• easy
• nonn

Comments

a(2n)=A001045(2n+1); a(2n+1)=A001045(2n) a(2n+2)=a(2n)+2*4^n; a(2n+3)=a(2n+1)+4^n.

Links

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

Programs

Mathematica

LinearRecurrence[{-1,4,4},{1,0,3},40] (* Harvey P. Dale, Dec 13 2022 *)

Python

def A092808(n): return ((1<Chai Wah Wu, Apr 18 2025

Formula

G.f.: (1+x-x^2)/((1+x)(1-2x)(1+2x)); E.g.f.: exp(-2x)/4+5exp(2x)/12+exp(-x)/3=cosh(2x)/2+exp(2x)/6+exp(-x)/3; a(n)=(-2)^n/4+5*2^n/12+(-1)^n/3.