A355075 - OEIS

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

(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

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) = 23.

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, 44, print1 (numerator(s+=fusc(n)/fusc(n+1))", ")) }

(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

CROSSREFS

Cf. A002487, A174868, A355076 (corresponding denominators).

Sequence in context: A069505 A363544 A373661 * A173878 A225264 A032403

Adjacent sequences: A355072 A355073 A355074 * A355076 A355077 A355078

KEYWORD

nonn,look,frac

AUTHOR

Rémy Sigrist, Jun 18 2022

STATUS

approved