Brian Hopkins answers his own 9-year-old question on the history of Fibonacci numbers and compositions (ordered partitions of integers): https://mathoverflow.net/a/362569/440
The ancient Indians knew that compositions into 1's and 2's are counted by Fibonacci numbers (e.g. the five compositions 2+2=2+1+1=1+2+1=1+1+2=1+1+1+1). Cayley knew compositions without 1 have the same counts. But who first knew that compositions with all parts odd are also counted by Fibonacci?
Hopkins suggests: de Morgan, 1846.
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