
06503239
j
2015f.00606
Koshy, Thomas
Gao, Zhenguang
A Fibonacci curiosity.
Math. Spectr. 48, No. 1, 1315 (2015).
2015
Applied Probability Trust (APT) c/o University of Sheffield, School of Mathematics and Statistics (SoMaS), Sheffield
EN
F60
Fibonacci numbers
Lucas formula
recursion
Summary: Using recursion, we establish that the sums $\sum_{k\ge 0,k\ \text{even}}{mk\choose k}$ and $\sum_{k\ge 0,k\ \text{odd}}{mk\choose k}$, which occur in the wellknown Lucas formula, are equal if and only if $m=3n1$.