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A355075 a(n) is the numerator of Sum_{k = 0..n} fusc(k)/fusc(k+1) (where fusc is Stern's diatomic series A002487).

%I A355075 #12 Jun 19 2022 18:42:24
%S A355075 0,1,3,7,23,16,6,9,37,127,671,821,169,63,33,41,207,439,3153,10439,
%T A355075 21193,22537,23137,26077,26317,27493,14009,5043,729,191,39,44,265,
%U A355075 1361,4133,8671,96101,694487,704189,750389,754169,1546453,20325649,4252517,4282547
%N A355075 a(n) is the numerator of Sum_{k = 0..n} fusc(k)/fusc(k+1) (where fusc is Stern's diatomic series A002487).
%H A355075 Rémy Sigrist, <a href="/A355075/b355075.txt">Table of n, a(n) for n = 0..8192</a>
%H A355075 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%e A355075 For n = 4:
%e A355075 - the first 5 terms of A002487 are: 0, 1, 1, 2, 1, 3,
%e A355075 - 0/1 + 1/1 + 1/2 + 2/1 + 1/3 = 23/6,
%e A355075 - so a(4) = 23.
%o A355075 (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 A355075 { s = 0; for (n=0, 44, print1 (numerator(s+=fusc(n)/fusc(n+1))", ")) }
%o A355075 (Python)
%o A355075 from fractions import Fraction
%o A355075 from functools import reduce
%o A355075 def A355075(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)).numerator # _Chai Wah Wu_, Jun 19 2022
%Y A355075 Cf. A002487, A174868, A355076 (corresponding denominators).
%K A355075 nonn,look,frac
%O A355075 0,3
%A A355075 _Rémy Sigrist_, Jun 18 2022