A341313 a(n) = (a(n-1) + a(n-3))/2^m, where 2^m is the highest power of 2 that divides both a(n-1) and a(n-3), with a(0) = a(1) = a(2) = 1.

1, 1, 1, 2, 3, 4, 3, 6, 5, 8, 7, 12, 5, 12, 6, 11, 23, 29, 40, 63, 92, 33, 96, 47, 80, 11, 58, 69, 80, 69, 138, 109, 178, 158, 267, 445, 603, 870, 1315, 1918, 1394, 2709, 4627, 6021, 8730, 13357, 19378, 14054, 27411, 46789, 60843, 88254, 135043, 195886, 142070, 277113, 472999

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 A341312.

It appears that the equation log(a(n)) = 0.265986*n + 1.56445 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(A341313) from linear fit in range 3...10000.

Maple

RK3:=proc(n) local t1, t2; option remember;
if n <= 2 then 1 else t1:=RK3(n-3)+RK3(n-1);
t2 := min( padic[ordp](RK3(n-3), 2), padic[ordp](RK3(n-1), 2) );
t1/2^t2;
fi;
end;
[seq(RK3(n), n=0..60)];

Prog

(PARI) a341313(nterms)={my(a=vector(nterms)); a[1]=a[2]=1; a[3]=2; for(n=4, nterms, a[n]=(a[n-1]+a[n-3])/2^min(valuation(a[n-1], 2), valuation(a[n-3], 2))); concat([1], a)};
a341313(60) \\ Hugo Pfoertner, Feb 16 2021

Crossrefs

Cf. A000930, A214551, A341312.

Sequence in context: A076945 A074792 A321168 * A341312 A347123 A318510

Adjacent sequences: A341310 A341311 A341312 * A341314 A341315 A341316

Keyword

nonn

Author

N. J. A. Sloane, Feb 16 2021

Status

approved