Cascade-free sequence counts for GEN/PROP/KILL digit operations satisfy a(L) = N a(L-1) - d a(L-2) and equal scaled Chebyshev polynomials, with base-3 doubling equaling the Fibonacci bisection F(2L+2).
Ribenboim,The New Book of Prime Number Records, 3rd ed., Springer, New York
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Cascade-free sequences, dispersion index, and state avoidance for stateful digit-wise operations
Cascade-free sequence counts for GEN/PROP/KILL digit operations satisfy a(L) = N a(L-1) - d a(L-2) and equal scaled Chebyshev polynomials, with base-3 doubling equaling the Fibonacci bisection F(2L+2).