A355075 -id:A355075

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A355076

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

+10
2

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

(list; graph; refs; listen; history; text; internal format)

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).

KEYWORD

nonn,look,frac

AUTHOR

Rémy Sigrist, Jun 18 2022

STATUS

approved

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