A355076 a(n) is the denominator of Sum_{k = 0..n} fusc(k)/fusc(k+1) (where fusc is Stern's diatomic series A002487).

1, 1, 2, 2, 6, 3, 1, 1, 4, 12, 60, 60, 12, 4, 2, 2, 10, 20, 140, 420, 840, 840, 840, 840, 840, 840, 420, 140, 20, 5, 1, 1, 6, 30, 90, 180, 1980, 13860, 13860, 13860, 13860, 27720, 360360, 72072, 72072, 72072, 8008, 8008, 72072, 72072, 72072, 360360, 27720

Offset: 0

Author

Rémy Sigrist, Jun 18 2022

Keywords

• nonn
• look
• frac

Examples

			For n = 4:
- the first 5 terms of A002487 are: 0, 1, 1, 2, 1, 3,
- 0/1 + 1/1 + 1/2 + 2/1 + 1/3 = 23/6,
- so a(4) = 6.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Index entries for sequences related to Stern's sequences

Crossrefs

Cf. A002487, A174868, A355075 (corresponding numerators).

Programs

PARI

fusc(n)=local(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); b \\ after Charles R Greathouse IV in A002487
{ s = 0; for (n=0, 52, print1 (denominator(s+=fusc(n)/fusc(n+1))", ")) }

Python

from fractions import Fraction
from functools import reduce
def A355076(n): return sum(Fraction(reduce(lambda x,y:(x[0],x[0]+x[1]) if int(y) else (x[0]+x[1],x[1]),bin(k)[-1:1:-1],(1,0))[1],reduce(lambda x,y:(x[0],x[0]+x[1]) if int(y) else (x[0]+x[1],x[1]),bin(k+1)[-1:1:-1],(1,0))[1]) for k in range(n+1)).denominator # Chai Wah Wu, Jun 19 2022

Formula

Conjecture: a(n) = 1 for n of the form 2*4^k - 1 or 2*4^k - 2 for some k >= 0.