%I #11 Dec 13 2022 18:29:30
%S 1,0,3,1,11,5,43,21,171,85,683,341,2731,1365,10923,5461,43691,21845,
%T 174763,87381,699051,349525,2796203,1398101,11184811,5592405,44739243,
%U 22369621,178956971,89478485,715827883,357913941,2863311531,1431655765
%N Pair reversal of Jacobsthal numbers.
%C 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.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,4,4).
%F 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.
%t LinearRecurrence[{-1,4,4},{1,0,3},40] (* _Harvey P. Dale_, Dec 13 2022 *)
%K easy,nonn
%O 0,3
%A _Paul Barry_, Mar 10 2004