Here are a few terms of the numerical sequence being generated, though I'm not sure how exactly they're being calculated or whether they're on the OEIS in some form:

`0, 9, 24, 37, 68, 79, 112, 168, 195, 207, 238, 294, 375, 421, 493, 619, 694, 757, 872, 1012`

I also tried the gaps between terms but no such luck:

`9, 15, 13, 31, 11, 33, 56, 27, 12, 31, 56, 81, 46, 72, 126, 75, 63, 115, 140`

I did it by finding the generation number at which the ships (excluding the first three) pass the still life I placed in the following pattern and dividing by 112:

`x = 1024, y = 731, rule = B3-ckq4z/S2-c3-a4iq5k6k`

3bo2bo$3b4o2$3b4o$3bo2bo3$2b2ob2o$3bobo$2bo3bo$2b2ob2o10$3b3o213b3o21b

3o309b3o93b3o21b3o69b3o21b3o93b3o21b3o21b3o21b3o57b3o9b3o$3b3o213b3o

21b3o309b3o93b3o21b3o69b3o21b3o93b3o21b3o21b3o21b3o57b3o9b3o$2bo3bo

211bo3bo19bo3bo307bo3bo91bo3bo19bo3bo67bo3bo19bo3bo91bo3bo19bo3bo19bo

3bo19bo3bo55bo3bo7bo3bo$2b2ob2o33bo177b2ob2o19b2ob2o307b2ob2o9bo81b2ob

2o19b2ob2o67b2ob2o19b2ob2o91b2ob2o19b2ob2o19b2ob2o19b2ob2o55b2ob2o7b2o

b2o$26b2ob2o9bo213b2ob2o235b2ob2o69bo117b2ob2o19b2ob2o19b2ob2o79b2ob2o

79b2ob2o61b2ob2o34b2o$27bobo225bobo237bobo189bobo21bobo21bobo81bobo81b

obo63bobo35bo$27bobo11bo213bobo237bobo71bo117bobo21bobo21bobo81bobo81b

obo63bobo$26b2ob2o10b2o211b2ob2o235b2ob2o70b2o115b2ob2o19b2ob2o19b2ob

2o79b2ob2o79b2ob2o61b2ob2o33bo2$1000b2o3bo7b2ob2o$999bobo3b2o6b7o$999b

o6bo5bo2bo3bo$999bobo15bobo$1000b2o5b2ob2o5b2o$1008bobo$962b3o3b3o37bo

bo$324bo636bo3bobo3bo35b2ob2o$324bo622b2o12b2ob2ob2ob2o$324bo621bo2bo

30bo$332b3o611bo2b2o29bo$302bo642bo2b2o30bo$302bo27bo614b4o$302bo27bo$

330bo2$316bo2bo629bo36b2o$316b4o628b2o34b2obo$401b3o81b3o81b3o81b3o81b

3o81b3o81b3o37b2o37b2o$316b4o664b2obo$316bo2bo666b2o8$946bo2bo$946b4o

2$946b4o$946bo2bo2$944b2o$942b2obo$942b2o$942b2obo$944b2o8$944b2o$942b

2obo$942b2o$942b2obo$944b2o2$946bo2bo$946b4o2$946b4o$946bo2bo2$944b2o$

942b2obo$942b2o$942b2obo$944b2o2$904bo2bo$904b4o2$904b4o$904bo2bo8$

902b2o$900b2obo$900b2o$900b2obo$902b2o20$902b2o$900b2obo$900b2o$900b2o

bo$902b2o8$862bo2bo$862b4o2$862b4o$862bo2bo14$860b2o$858b2obo$858b2o$

858b2obo$860b2o2$862bo2bo$862b4o2$862b4o$862bo2bo2$860b2o$858b2obo$

858b2o$858b2obo$860b2o2$823bo$822b2o$819b2o10$820bo2bo$820b4o2$820b4o$

820bo2bo20$781bo36b2o$780b2o34b2obo$777b2o37b2o$816b2obo$818b2o8$778bo

2bo$778b4o2$778b4o$778bo2bo2$776b2o$774b2obo$774b2o$774b2obo$776b2o8$

776b2o$774b2obo$774b2o$774b2obo$776b2o2$778bo2bo$778b4o2$778b4o$778bo

2bo2$776b2o$774b2obo$774b2o$774b2obo$776b2o2$736bo2bo$736b4o2$736b4o$

736bo2bo8$734b2o$732b2obo$732b2o$732b2obo$734b2o20$734b2o$732b2obo$

732b2o$732b2obo$734b2o8$694bo2bo$694b4o2$694b4o$694bo2bo14$692b2o$690b

2obo$690b2o$690b2obo$692b2o2$694bo2bo$694b4o2$694b4o$694bo2bo2$692b2o$

690b2obo$690b2o$690b2obo$692b2o2$655bo$654b2o$651b2o10$652bo2bo$652b4o

2$652b4o$652bo2bo20$613bo36b2o$612b2o34b2obo$609b2o37b2o$648b2obo$650b

2o8$610bo2bo$610b4o2$610b4o$610bo2bo2$608b2o$606b2obo$606b2o$606b2obo$

608b2o8$608b2o$606b2obo$606b2o$606b2obo$608b2o2$610bo2bo$610b4o2$610b

4o$610bo2bo2$608b2o$606b2obo$606b2o$606b2obo$608b2o2$568bo2bo$568b4o2$

568b4o$568bo2bo8$566b2o$564b2obo$564b2o$564b2obo$566b2o20$566b2o$564b

2obo$564b2o$564b2obo$566b2o8$526bo2bo$526b4o2$526b4o$526bo2bo14$524b2o

$522b2obo$522b2o$522b2obo$524b2o2$526bo2bo$526b4o2$526b4o$526bo2bo2$

524b2o$522b2obo$522b2o$522b2obo$524b2o2$487bo$486b2o$483b2o10$484bo2bo

$484b4o2$484b4o$484bo2bo20$445bo36b2o$444b2o34b2obo$441b2o37b2o$480b2o

bo$482b2o8$442bo2bo$442b4o2$442b4o$442bo2bo2$440b2o$438b2obo$438b2o$

438b2obo$440b2o8$440b2o$438b2obo$438b2o$438b2obo$440b2o2$442bo2bo$442b

4o2$442b4o$442bo2bo2$440b2o$438b2obo$438b2o$438b2obo$440b2o2$400bo2bo$

400b4o2$400b4o$400bo2bo8$398b2o$396b2obo$396b2o$396b2obo$398b2o20$398b

2o$396b2obo$396b2o$396b2obo$398b2o8$358bo2bo$358b4o2$358b4o$358bo2bo

14$356b2o$354b2obo$354b2o$354b2obo$356b2o2$358bo2bo$358b4o2$358b4o$

358bo2bo2$356b2o$354b2obo$354b2o$354b2obo$356b2o2$319bo$318b2o$315b2o

10$316bo2bo$316b4o2$316b4o$316bo2bo20$314b2o$312b2obo$312b2o$312b2obo$

314b2o!

If we're going to submit this to OEIS as a new sequence, we will need a few more terms so if anyone wants to make a script to calculate the terms I'd appreciate it.