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

0,3

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Index entries for sequences related to Stern's sequences

Formula

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A342628 A329380 A348146 * A344007 A130478 A308140

Adjacent sequences: A355073 A355074 A355075 * A355077 A355078 A355079

Keyword

nonn,look,frac

Author

Rémy Sigrist, Jun 18 2022

Status

approved