Interesting question. There are multiple answers.

1. The perfectly smooth shifting pattern
This is based on the concept that you both don't want to shift when gear change is less than 2% and don't want to jump gears with change greater than say 14%. Enter your 3 chainring tooth count on the top list and then enter the tooth count of each spocket in the bottom list. Site is http://www.panix.com/~jbarrm/cycal/cycal.30f.html.

You will have to process the numbers many times to find the ideal pattern.
1.1 remove duplicate gears, change less than 1%
1.2 start from bottom and slowly deselect gears until you find your shifting pattern.
1.3 The answer will involve some number, 2-4 usually, double shifts and require posting a shifting memory card
on your bike where you can refer to it.

2. After you have answer #1, it will usually favor one chainring. Redo the exercise until you have the best options for using
2.1 the low chainring being primary
2.2 the middle chainring being primary
2.3 the high chainring being primary
If you have lots of hills, answer to 2.1 may be best for you. If young and full of muscles, you might like 2.3. For most of us 2.2 will be the best.

3. The practical shifting pattern.
This approach say, forget double shifting as much as possible and forget a shifting index card. Ride in the middle chainring as much as possible and only downshift when hills are too steep or upshift when downhills run away with your legs. Just for fun, use the above site, your standard chainrings and try switching in different cassettes. Then look at just the middle ring and see the %change between gears and total range of gears each cassette gives you. For example an 11-34 gives you a wide range of speeds without shifting, but at a cost of harder changes between gears. A 12-23 gives you a narrower range of speeds, but shifting is like cutting butter with a hot knife.