OFFSET
3,1
COMMENTS
This sequence is bounded between floor((n-1)^2/sqrt(2) - 1) and (n-1)^2.
This sequence is the maximum dimension of a subspace of C^n * C^n (where * is the tensor/Kronecker product) that can be shown to be entangled by the first level of the hierarchy described in the linked Johnston-Lovitz-Vijayaraghavan paper.
LINKS
N. Johnston, B. Lovitz, and A. Vijayaraghavan. Complete hierarchy of linear systems for certifying quantum entanglement of subspaces. Physical Review A, 106:062443, 2022.
FORMULA
a(n) ~ (n-1)^2/sqrt(2).
PROG
(Python)
from math import isqrt
def A352940(n): return (isqrt(n**2*(n*(2*n-4)+2)+1)-1)//2 # Chai Wah Wu, May 07 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Nathaniel Johnston, May 06 2022
STATUS
approved