OFFSET
0,4
COMMENTS
It will be interesting to compare the growth rates of A000930 (well-understood), A241551 (a mystery), the present sequence, and A341313.
It appears that the equation log(a(n)) = 0.296869*n - 4.69131 is a good fit to the data (see the figures). - Hugo Pfoertner, Feb 17 2021
LINKS
Hugo Pfoertner, Table of n, a(n) for n = 0..5000
Hugo Pfoertner, Comparison of linear fits to logarithm of A341312, A341313, A214551 (Reed Kelly), and A000930 (Narayana's cows).
Hugo Pfoertner, Deviation of log(A341312) from linear fit in range 3...10000.
MAPLE
RK2:=proc(n) local t1; option remember;
if n <= 2 then 1 else t1:=RK2(n-3)+RK2(n-1);
if (RK2(n-3) mod 2) = 0 and (RK2(n-1) mod 2) = 0 then t1:=t1/2; fi;
t1; fi; end;
[seq(RK2(n), n=0..60)];
PROG
(PARI) a341312(nterms)={my(a=vector(nterms)); a[1]=a[2]=1; a[3]=2; for(n=4, nterms, a[n]=if(a[n-1]%2==0&&a[n-3]%2==0, (a[n-1]+a[n-3])/2, a[n-1]+a[n-3])); concat([1], a)};
a341312(60) \\ Hugo Pfoertner, Feb 17 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 16 2021
STATUS
approved