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

0,3

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

Table of n, a(n) for n=0..33.

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

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.

Mathematica

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

Crossrefs

Sequence in context: A165674 A027446 A027516 * A343171 A113955 A110165

Adjacent sequences: A092805 A092806 A092807 * A092809 A092810 A092811

Keyword

easy,nonn

Author

Paul Barry, Mar 10 2004

Status

approved