|
%I #19 Feb 17 2021 20:24:58
%S 1,1,1,2,3,4,3,6,5,8,7,12,10,17,29,39,56,85,124,90,175,299,389,564,
%T 863,1252,908,1771,3023,3931,5702,8725,12656,9179,17904,15280,24459,
%U 42363,57643,82102,124465,182108,132105,256570,219339,351444,304007,523346,437395,741402,632374
%N a(n) = a(n-1) + a(n-3) unless a(n-1) and a(n-3) are both even in which case a(n) = (a(n-1) + a(n-3))/2, with a(0) = a(1) = a(2) = 1.
%C A sequence intermediate between Narayana's A000930 and Reed Kelly's A214551.
%C It will be interesting to compare the growth rates of A000930 (well-understood), A241551 (a mystery), the present sequence, and A341313.
%C 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
%H Hugo Pfoertner, <a href="/A341312/b341312.txt">Table of n, a(n) for n = 0..5000</a>
%H Hugo Pfoertner, <a href="/A341312/a341312.pdf">Comparison of linear fits to logarithm of A341312, A341313, A214551 (Reed Kelly), and A000930 (Narayana's cows)</a>.
%H Hugo Pfoertner, <a href="/A341312/a341312_1.pdf">Deviation of log(A341312) from linear fit in range 3...10000</a>.
%p RK2:=proc(n) local t1; option remember;
%p if n <= 2 then 1 else t1:=RK2(n-3)+RK2(n-1);
%p if (RK2(n-3) mod 2) = 0 and (RK2(n-1) mod 2) = 0 then t1:=t1/2; fi;
%p t1; fi; end;
%p [seq(RK2(n),n=0..60)];
%o (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)};
%o a341312(60) \\ _Hugo Pfoertner_, Feb 17 2021
%Y Cf. A000930, A214551, A341313.
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Feb 16 2021
|
