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Infinitely many.

For example:

Un+1 = Un + 3

or

Un+1 = 2*Un - 1

or

Un+1 = 3*Un - 5

or, more generally,

Un+1 = k*Un + 7 - 4*k where k is any number.

Each one of them will be different from the third term onwards. These are linear patterns. There are quadratic and other recursive relationships.

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12y ago

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