OFFSET

0,5

COMMENTS

This sequence has similarities with A090706; here we consider multisets of run-lengths, there multisets of digits in binary expansions.

LINKS

FORMULA

a(n) = 1 iff n = 0 or n belongs to A140690.

EXAMPLE

For n = 18:

- the binary expansion of 18 is "10010",

- the corresponding multiset of run-lengths is m = (1, 2, 1, 1),

- m has 4 terms: 3 times "1" and once "2",

- so a(18) = 4! / (3! * 1!) = 4.

PROG

(PARI) a(n) = { my (r=[]); while (n, my (v=valuation(n+n%2, 2)); n\=2^v; r=concat(v, r)); my (s=Set(r), f=vector(#s)); for (k=1, #r, f[setsearch(s, r[k])]++); (#r)! / prod(k=1, #f, f[k]!) }

(Python)

from math import factorial, prod

from itertools import groupby

from collections import Counter

def A361477(n): return factorial(len(c:=[len(list(g)) for k, g in groupby(bin(n)[2:])]))//prod(map(factorial, Counter(c).values())) # Chai Wah Wu, Mar 16 2023

CROSSREFS

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Mar 13 2023

STATUS

approved