A355075 a(n) is the numerator of Sum_{k = 0..n} fusc(k)/fusc(k+1) (where fusc is Stern's diatomic series A002487).
0, 1, 3, 7, 23, 16, 6, 9, 37, 127, 671, 821, 169, 63, 33, 41, 207, 439, 3153, 10439, 21193, 22537, 23137, 26077, 26317, 27493, 14009, 5043, 729, 191, 39, 44, 265, 1361, 4133, 8671, 96101, 694487, 704189, 750389, 754169, 1546453, 20325649, 4252517, 4282547
Offset: 0
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) = 23.
Links
Programs
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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, 44, print1 (numerator(s+=fusc(n)/fusc(n+1))", ")) }
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Python
from fractions import Fraction from functools import reduce 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