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Home / Number with at least one "11": let’s use recurrence:

Number with at least one "11": let’s use recurrence:

February 22, 2026

Number with at least one "11": let’s use recurrence:

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And 13 is correct.
But let’s cross-check with inclusion:
Total: 32
Let \(c_n\) = number of binary strings of length \(n\) with no two consecutive 1’s.
We know: \(c_n = c_{n-1} + c_{n-2}\), \(c_1 = 2\), \(c_2 = 3\)
\(c_3 = 3 + 2 = 5\)

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