How many ways are there to form a row of ten face-up cards, disregarding values,
so that there are no adjacent red cards? The answer,
which turns
out to be 144, involves the standard Fibonacci sequence. This starts with
seeds 1, 1, and then adds two consecutive terms to determine subsequent terms:

1

1

2

3

5

8

13

21

34

55

89

144

...

Starting with arbitrary seeds yields what are sometimes known as Gibonacci (for
generalized Fibonacci) sequences, e.g., see Art Benjamin and Jennifer Quinn's
delightful MAA book