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We critically analyse a recent numerical method due to the first author,Rechnitzer and van Rensburg, which attempts to detect amenability ornon-amenability in a finitely generated group by numerically estimating itsasymptotic cogrowth rate. We identify two potential sources of error. We thenpropose a modification of the method that enables it to easily computesurprisingly accurate estimates for initial terms of the cogrowth sequence.

Sub-dominant cogrowth behaviour and the viability of deciding amenability numerically