Mistake: formula \(\binom{n-k+1}{k}\) is for placing \(k\) non-adjacent indistinct items? No — standard formula for number of binary strings of length \(n\) with no two consecutive 1’s is \(F_{n+2}\), where \(F_1=1, F_2=1, F_3=2, F_4=3, F_5=5, F_6=8, F_7=13, F_8=21\)

Sun, 03 May 2026 13:43:18 +0000

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