TLDWTR: Based off my experience you need to do 600 defiant engrams along with needing -blam!- glimmer for the focusing to get all the recovered leviathan patterns. I recently had an abundance of defiant engrams after finishing off my seasonal weapon pattern progress so i focused them all on the recovered leviathan weapons, id done this in the past and gotten 2 of 5 for the sword and 3 of 5 for the shotty. Anyways i had 79 engrams and focused them 39 times for 29 shotguns and 10 swords which seems to be a bit too far of a gap to be mere chance. Anyways i managed to get 1 sword red border and 2 shotgun red borders completing the shotty. So assuming the 1 in 10 red border chance ive heard tossed around and given that i did get 1 red border for 10 swords. This would mean youd need to focus 50 swords to get a pattern done, which using the ratio outlined above (29 shottys to 10 swords would be about 3 shotguns to 1 sword) would result in 150 shotguns. Add onto that that there are 3 swords you need progress for and you can effectively triple that to 150 swords to 450 shotguns, resulting in needing to focus 600 times to complete all the sword patterns which would require 1200 (aka 600 activities completed and it seems like they recently made the engrams drop only about 1 in 2 times after you get a certain amount, I did flawless ron and wiped a bunch and started not getting engrams from the first encounter sometimes, which would then make you have to do 1200 activities for the engrams even with the double engram war table upgrade) defiant engrams and 600 legendary shards worth of glimmer (1k glimmer per focus times 600 focuses equals 600,000 glimmer, 10k glimmer for 10 shards which translates to 1k glimmer = 1 shard and since there is 600,000 needed to focus that equals 600 shards)