if you're interested in this (or really any other kind of) sequence, you should consult the online encyclopedia of integer sequences:
https://oeis.org/A283564

a general analysis of the sequence can be found in the linked original paper by Andrew Bremner and Allan Macleod. the solutions themselves, such as the one reero posted for n = 4, can be found in the mathoverflow link. Allan, one of the aforementioned authors, also chimed in.

this sequence is analytically tackled through algebraic topology & specific solutions can be found by plugging a generator into a Computer Algebra System.

can u hook me up with some turks i never found any turks

the more you guys bump this thread with inane shit, the better he'll feel about himself. no, he isn't going "insane"; no, his life isn't "falling apart" as a result of this. and, more importantly, he plays nothing like a good invite scout. he is not good practice, and he will actually make you play worse in the long-run because he toggles his hacks just enough to keep you playing against him (i.e. he allows himself a buffer that he tries to catch up to). stop posting his retarded videos. he enjoys every single bit of attention, and the only acceptable trade-off we can make is posting just enough information to get him banned.
in other words, it'd honestly be best if this thread was solely reserved for his presence on mge/dm servers which i'm happy to address to the best of my abilities.
anyone that hacks for thousands of hours needs to be dealt with in a methodical, cold manner.

Saturday, June 10, 2017
11:30 PM - trampler of the vast expanse: hey, just wanted to let you know that the merlow kid is hacking on your mge server. if you get a minute, could you ban him? annoying that people are adding up against him and giving him attention.
11:30 PM - trampler of the vast expanse: http://steamcommunity.com/profiles/76561198301088133
11:31 PM - FROYO b4nny.tv: i banned him earlier i think
11:31 PM - trampler of the vast expanse: ah, his name is bolin on the server at the moment. something may have been misapplied.
11:31 PM - FROYO b4nny.tv: i banned the other one
11:31 PM - FROYO b4nny.tv: i guess
11:31 PM - FROYO b4nny.tv: supposedly there are two
11:32 PM - trampler of the vast expanse: nah, the same account i posted on the forums is the one playing. definitely could've been one of his friends playing earlier under that name to try to be the sacrificial lamb so his main account can play, so to speak
11:32 PM - FROYO b4nny.tv is now playing Team Fortress 2. Click here to join.
11:32 PM - FROYO b4nny.tv: if hes there right now i can ban him
11:32 PM - trampler of the vast expanse: yeah, he is
11:32 PM - FROYO b4nny.tv: what evidence do you have btw?
11:33 PM - FROYO b4nny.tv is now playing Team Fortress 2. Click here to join.
11:33 PM - trampler of the vast expanse: lots of banlists other than the firepowered one
11:33 PM - trampler of the vast expanse: and good judgment of character due to multiple videos on his youtube account talking about hacking -- he's been banned on multiple tf2 servers on the current account due to anti-cheat detection
11:33 PM - trampler of the vast expanse: detected due to lua manipulation and/or detected due to trying to use sv_pure bypass
11:34 PM - trampler of the vast expanse: the nullcore cheat can look nearly legitimate if someone "practices" with it enough unfortunately. the mathematics of kinematic prediction are well understood
11:35 PM - trampler of the vast expanse: and, to clarify, he was auto-banned on another server because he was joined in a private nullcore group
11:35 PM - trampler of the vast expanse: which he shortly left after the ban
11:35 PM - FROYO b4nny.tv: k
11:36 PM - FROYO b4nny.tv is now playing Team Fortress 2. Click here to join.
11:38 PM - trampler of the vast expanse: awesome, i saw that he got banned. thanks a bunch. good luck on your stream tonight
11:38 PM - FROYO b4nny.tv: ty

thank you again to b4nny for the prompt response even while streaming. i think those are most of the major mge servers. expect him on vatican in the future -- i'll handle that when the time comes.

he's actually a global war historian and it's short for apartheid: prejudiced terror

FABLE'S MY FAVORITE INVITE TEAM WOOOOO

5' 7"
i wish i was taller so i could have a better gaming posture
most desks i've used (besides the one at my place) are too tall for me to comfortably arm aim :(

whoa

yeah, there was some sort of miscommunication; his Captain Strong account was banned instead of his new account. merlow realized this and switched his alias & steam avatar to temporarily avoid detection. it has been corrected & his current account is properly banned.

10:24 PM - Nimbus: you can tell your friends who wanted to see this ban that its happening
10:26 PM - Nimbus: he is banned
10:28 PM - Nimbus: he is gonna try to ban him through source mod as well

thank you to nimbus & nacho for promptly investigating him and banning him.

UPDATE:
thank you to nimbus & nacho for promptly investigating him and banning him.

10:24 PM - Nimbus: you can tell your friends who wanted to see this ban that its happening
10:26 PM - Nimbus: he is banned
10:28 PM - Nimbus: he is gonna try to ban him through source mod as well

http://steamcommunity.com/profiles/76561198301088133
https://www.firepoweredgaming.com/sourcebans/index.php?p=banlist&advSearch=STEAM_0:1:170411202&advType=steamid
this was his old account that he used to cheat on dm servers with (and yes, he's the same guy that had tons of threads about his cheating on the tf.tv dm servers): http://steamcommunity.com/profiles/76561198339552712
i honestly shouldn't have to make this thread since i know he gets off to it, but there are a shocking number of good players without critical thinking faculties that give this humongous retard the benefit of the doubt.
the worst part is that he has deluded a bunch of new players in ugc that he's not cheating. he's an extremely bad influence to the small amount of competitive newcomers & he needs to get the fuck out of the game.
for now, do not add up against him. do not let him enjoy any part of cheating. do not give him an iota of your time. if he ever joins, isolate him until he leaves the server.

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yeah cuz i promised her i would win?? duh their just parents easy to convince?? if ur a hypercompetative u would give up anything to be the top and my only life gole si to be a tf2 invite

lol its patehetic that u guys arent playing invite my mom let me drop out of skool so i can play invite wat r u pussies??

if you use the english language but aren't absorbed in studying english, don't use it.
that goes for anything english.