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A352940
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The largest positive integer k such that binomial(k+1,2) <= binomial(n,2)^2.
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1
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3, 8, 13, 20, 29, 39, 50, 63, 77, 92, 109, 128, 147, 169, 191, 215, 241, 268, 296, 326, 357, 389, 423, 459, 495, 534, 573, 614, 657, 700, 746, 792, 840, 890, 941, 993, 1047, 1102, 1159, 1217, 1276, 1337, 1399, 1463, 1528, 1594, 1662, 1731, 1802, 1874, 1948
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OFFSET
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3,1
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) ~ (n-1)^2/sqrt(2).
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PROG
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(Python)
from math import isqrt
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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