This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A352940 #153 May 24 2023 13:21:21 %S A352940 3,8,13,20,29,39,50,63,77,92,109,128,147,169,191,215,241,268,296,326, %T A352940 357,389,423,459,495,534,573,614,657,700,746,792,840,890,941,993,1047, %U A352940 1102,1159,1217,1276,1337,1399,1463,1528,1594,1662,1731,1802,1874,1948 %N A352940 The largest positive integer k such that binomial(k+1,2) <= binomial(n,2)^2. %C A352940 This sequence is bounded between floor((n-1)^2/sqrt(2) - 1) and (n-1)^2. %C A352940 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. %H A352940 N. Johnston, B. Lovitz, and A. Vijayaraghavan. <a href="https://arxiv.org/abs/2210.16389">Complete hierarchy of linear systems for certifying quantum entanglement of subspaces</a>. Physical Review A, 106:062443, 2022. %F A352940 a(n) ~ (n-1)^2/sqrt(2). %o A352940 (Python) %o A352940 from math import isqrt %o A352940 def A352940(n): return (isqrt(n**2*(n*(2*n-4)+2)+1)-1)//2 # _Chai Wah Wu_, May 07 2022 %K A352940 nonn %O A352940 3,1 %A A352940 _Nathaniel Johnston_, May 06 2022