Fibonacci Number as Sum of Binomial Coefficients/Mistake/Second Edition

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Source Work

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary
$5$


Mistake

Lucas discovered a relationship between Fibonacci numbers and the binomial coefficients:
$F_{n + 1} = \dbinom n 0 + \dbinom {n - 1} 1 + \dbinom {n - 2} 1 + \cdots$


Correction

The given expression is a misprint for:

$F_{n + 1} = \dbinom n 0 + \dbinom {n - 1} 1 + \dbinom {n - 2} 2 + \cdots$


Interestingly and oddly, this is correct in the first edition of Curious and Interesting Numbers of $1986$.


Sources