Averaged meta-Fibonacci recursions at critical alpha=1 exhibit a triangular block structure where k appears k times, yielding Q(n) ~ sqrt(2n), while supercritical alpha>1 forces any linear growth rate to equal 1 - 1/alpha.
III Chew, and Stephen M
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Critical Slow Growth in Averaged Meta-Fibonacci Recursions
Averaged meta-Fibonacci recursions at critical alpha=1 exhibit a triangular block structure where k appears k times, yielding Q(n) ~ sqrt(2n), while supercritical alpha>1 forces any linear growth rate to equal 1 - 1/alpha.