A341312 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.

1, 1, 1, 2, 3, 4, 3, 6, 5, 8, 7, 12, 10, 17, 29, 39, 56, 85, 124, 90, 175, 299, 389, 564, 863, 1252, 908, 1771, 3023, 3931, 5702, 8725, 12656, 9179, 17904, 15280, 24459, 42363, 57643, 82102, 124465, 182108, 132105, 256570, 219339, 351444, 304007, 523346, 437395, 741402, 632374

Offset

0,4

Comments

A sequence intermediate between Narayana's A000930 and Reed Kelly's A214551.

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

Cf. A000930, A214551, A341313.

Sequence in context: A074792 A321168 A341313 * A347123 A318510 A048276

Adjacent sequences: A341309 A341310 A341311 * A341313 A341314 A341315

Keyword

nonn

Author

N. J. A. Sloane, Feb 16 2021

Status

approved