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ozo, also, this a[n]=a[n-1]+a[n-2]+a[n-3] gives us the n-digit numbers which can be created using only digits 5 and 9, where no three ones stand side by side. (but this does not mentioned in OEIS)<br />
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Could you explain why this sequence solves my original question? For better understanding.
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ozo, also, this a[n]=a[n-1]+a[n-2]+a[n-3] gives us the n-digit numbers which can be created using only digits 5 and 9, where no three ones stand side by side. (but this does not mentioned in OEIS)

Could you explain why this sequence solves my original question? For better understanding.

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How many n-digit numbers can be created using only digits 5 and 9, where no four identical digits stand side by side?
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How many n-digit numbers can be created using only digits 5 and 9, where no four identical digits stand side by side?

n-digit numbers created using digits 5 and 9, where no four identical digits stand side by side.

An algorithm is a self-contained step-by-step set of operations to be performed. Algorithms exist that perform calculation, data processing, and automated reasoning. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.