Generate the Rummy Sequence
JavaScript ES6, 94 92 72 70 66 64 bytes

Saved 6 bytes thanks to Neil!

n=&gt;[...Array(a=Math.sqrt(8*n+1)-1&gt;&gt;1)].map((_,l)=&gt;l&lt;n-a*(a+1)/2)


I don't think this can be golfed more. At least with the equations.

Explanation

They are two main equations (n is input):

(Math.sqrt(8*n+1)-1)/2


This will give the total size the output array will need to be. In my program I used &gt;&gt;1 instead of (...)/2 these are the same as the first bit in binary has a value of 2. Shifting it will result in in floor(.../2)



n-a*(a+1)/2


This is the amount of trues there will be. a is the result of the previous expression.



This is what the syntax does:

[...Array(n)]


This code generates an array with range [0, n) in this answer n is the first equation.



.map((_,l)=&gt;l&lt;n) this will loop through the above range, l is the variable containing the current item in the range. If the item is less than the amount of trues they are (determined by second equation), then it will return true, else false.