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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).

%I A355076 #11 Jun 19 2022 18:42:56
%S A355076 1,1,2,2,6,3,1,1,4,12,60,60,12,4,2,2,10,20,140,420,840,840,840,840,
%T A355076 840,840,420,140,20,5,1,1,6,30,90,180,1980,13860,13860,13860,13860,
%U A355076 27720,360360,72072,72072,72072,8008,8008,72072,72072,72072,360360,27720
%N A355076 a(n) is the denominator of Sum_{k = 0..n} fusc(k)/fusc(k+1) (where fusc is Stern's diatomic series A002487).
%H A355076 Rémy Sigrist, <a href="/A355076/b355076.txt">Table of n, a(n) for n = 0..8192</a>
%H A355076 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F A355076 Conjecture: a(n) = 1 for n of the form 2*4^k - 1 or 2*4^k - 2 for some k >= 0.
%e A355076 For n = 4:
%e A355076 - the first 5 terms of A002487 are: 0, 1, 1, 2, 1, 3,
%e A355076 - 0/1 + 1/1 + 1/2 + 2/1 + 1/3 = 23/6,
%e A355076 - so a(4) = 6.
%o A355076 (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
%o A355076 { s = 0; for (n=0, 52, print1 (denominator(s+=fusc(n)/fusc(n+1))", ")) }
%o A355076 (Python)
%o A355076 from fractions import Fraction
%o A355076 from functools import reduce
%o A355076 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
%Y A355076 Cf. A002487, A174868, A355075 (corresponding numerators).
%K A355076 nonn,look,frac
%O A355076 0,3
%A A355076 _Rémy Sigrist_, Jun 18 2022