Question on A057960

[franktaw at netscape.net]

All published terms of A057960 satisfy a(n) = floor(a(n-1)*(a(n-1)+1/2)/a(n-2).  (In fact, I have verified the next 7 terms as well.)  Note that for A057960, a(n) = floor(a(n-1)*(sqrt(3)+1)).  (This is the formula from DELEHAM Philippe - writing sqrt(3) as "3^0, 5" - ugh.)
 
Can anyone prove that this recurrence does, in fact, produce this sequence?
 
Franklin T. Adams-Watters
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