OFFSET
0,6
COMMENTS
Permuting the symbols will not change the structure.
a(n) = A056481(n) for n > 1. - Jonathan Frech, May 21 2021
REFERENCES
M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..5000
FORMULA
a(n) = Sum_{d|n} mu(d)*A016116(n/d-1) for n > 0.
a(n) = Sum_{k=1..2} A284826(n, k) for n > 0. - Andrew Howroyd, May 21 2021
a(n) = A056458(n)/2 for n>=1. - Alois P. Heinz, Feb 18 2025
EXAMPLE
Example from Jonathan Frech, May 21 2021: (Start)
The a(9)=14 lexicographically earliest equivalence class members in the alphabet {0,1} are:
000010000
000101000
000111000
001000100
001010100
001101100
001111100
010000010
010101010
010111010
011000110
011010110
011101110
011111110
(End)
MATHEMATICA
Table[DivisorSum[n, MoebiusMu[#]*2^Floor[(n/# - 1)/2] &], {n, 46}] (* Michael De Vlieger, May 21 2021 *)
PROG
(PARI) a(n) = if(n==0, 1, sumdiv(n, d, moebius(d)*2^((n/d-1)\2))) \\ Andrew Howroyd, May 21 2021
(Python)
from sympy import mobius, divisors
def A056476(n): return sum(mobius(n//d)<<(d-1>>1) for d in divisors(n, generator=True)) if n else 1 # Chai Wah Wu, Feb 18 2024
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
EXTENSIONS
Definition clarified by Jonathan Frech, May 21 2021
a(0)=1 prepended and a(32)-a(45) from Andrew Howroyd, May 21 2021
STATUS
approved