%I #9 Mar 15 2024 05:38:43
%S 0,1,2,8,22,70,202,622,1844,5576,16658,50114,150140,450824,1351850,
%T 4056794,12168538,36509302,109522330,328578142,985717768,2957186620,
%U 8871509746,26614629466,79843738258,239531515054,718594094338
%N Number of ternary words of length n (beginning 0) with autocorrelation function 2^(n-1)+1.
%F a(2n) = 3*a(2n-1) + 2*a(n) for n >= 2; a(2n-1) = 3*a(2n-2) - a(n) for n >= 2
%p A045695 := proc(n)
%p if n <=2 then
%p n-1 ;
%p elif type(n,'even') then
%p 3*procname(n-1)+2*procname(n/2) ;
%p else
%p 3*procname(n-1)-procname((n+1)/2) ;
%p end if;
%p end proc: # _R. J. Mathar_, Oct 04 2014
%t a[n_] := If[n <= 2, n-1,
%t If[EvenQ[n], 3*a[n-1] + 2*a[n/2],
%t 3*a[n-1] - a[(n+1)/2]]];
%t Table[a[n], {n, 1, 27}] (* _Jean-François Alcover_, Mar 15 2024, after Maple code *)
%K nonn
%O 1,3
%A TORSTEN.SILLKE(AT)LHSYSTEMS.COM