Sequence of 2-color combinations

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I'm crafting flowers made of two colors, a petal color and a center color. I have 5 colors total: yellow, green, pink, orange, and blue.

I have already made flowers with these color combinations:

  1. Pink petals, yellow center
  2. Yellow petals, green center
  3. Green petals, orange center
  4. Orange petals, blue center

I would like to create flowers with all possible combinations* of two distinct colors, but there are a few conditions for the sequence.

  • The center color of the previous flower becomes the petal color of the next one.
  • The same color should never be used 3 times in a row.
  • As much as possible, I would like to maintain a consistent gap between when each color appears.

Please help me find the best sequence of flowers that picks up where I left off above! If you do, my math PhD friends will be so annoyed someone else did it first!

*All possible combinations means a pink petal, yellow center flower and a yellow petal, pink center flower are distinct.