The Fibonacci Series

Form a series x_n by taking the position in the alphabet of each letter in Fibonacci’s name:

x_n = 6,  9,  2,  15,  14,  1,  3,  3,  9                   for n from 1 to 9.

Then form a second series y_n by the relationship

y_n = a₀ + a₁x_n + a₂x_n² + a₃x_n³ + a₄x_n⁴ + a₅x_n⁵ + a₆x_n⁶,

where the a’s are the well-known Traho-Cruris coefficients: 

a₀ = 83

a₁ = –136.518

a₂ = 78.96

a₃ = –19.6321

a₄ = 2.327465

a₅ = –0.1297512

a₆ = 0.00273576

This forms the series:

y_n = 1,  1,  2,  3,  5,  8,  13,      for  n from 1 to 7.

which is known as the “Fibonacci series.”