A332917 A332916(n)/2^a(n) is the average number of binary strings of length n with Levenshtein distance <= 3 from a uniform randomly sampled binary string of this length.

0, 1, 4, 4, 6, 5, 8, 8, 10, 8, 12, 12, 14, 13, 16, 16, 18, 15, 20, 20, 22, 21, 24, 24, 26, 24, 28, 28, 30, 29, 32, 32, 34, 30, 36, 36, 38, 37, 40, 40, 42, 40, 44, 44, 46, 45, 48, 48, 50, 47, 52, 52, 54, 53, 56, 56, 58, 56, 60, 60, 62, 61, 64, 64, 66, 61, 68, 68

Offset

3,3

Comments

See A332916 for more information.

Links

Table of n, a(n) for n=3..70.

Prog

(PARI) f(n)=(40+6*n-4*n^2)/2^n-83/2+331/12*n-6*n^2+2/3*n^3;
for(k=3, 70, print1(round(log(denominator(f(k)))/log(2)), ", "))
(Python)
from fractions import Fraction
def f(n): return Fraction(40+6*n-4*n**2, 2**n) - Fraction(83, 2) + Fraction(331*n, 12) - 6*n**2 + Fraction(2*n**3, 3)
def a(n): return (f(n).denominator).bit_length() - 1
print([a(n) for n in range(3, 71)]) # Michael S. Branicky, Aug 31 2021

Crossrefs

Cf. A332916, A332918.

Sequence in context: A071256 A078240 A296844 * A016710 A225134 A121064

Adjacent sequences: A332914 A332915 A332916 * A332918 A332919 A332920

Keyword

nonn,frac

Author

Hugo Pfoertner, Mar 05 2020

Status

approved