Compression #2 - notes

Here are notes on maximum bits in a larger area. This for example, says that if you have 12 active (on bits) in a 32bit area, there will be X combinations.

32:1 - 32 (5)
32:2 - 496 (9)
32:3 - 4960 (13)
32:4 - 35960 (16)
32:5 - 201376 (18)
32:6 - 906192 (20)
32:7 - 3365856 (22)
32:8 - 10518300 (24)
32:9 - 28048800 (25)
32:10 - 64512240 (26)
32:11 - 129024480 (27)
32:12 - 225792840 (28)
32:13 - 347373600 (29)
32:14 - 471435600 (29)
32:15 - 565722720 (30)
32:16 - 601080390 (30)
32:17 - 565722720 (30)
32:18 - 471435600 (29)
32:19 - 347373600 (29)
32:20 - 225792840 (28)
32:21 - 129024480 (27)
32:22 - 64512240 (26)
32:23 - 28048800 (25)
32:24 - 10518300 (24)
32:25 - 3365856 (22)
32:26 - 906192 (20)
32:27 - 201376 (18)
32:28 - 35960 (16)
32:29 - 4960 (13)
32:30 - 496 (9)
32:31 - 32 (5)
32:32 - 1 (0)

These are the values i've come across using a set of functions. 32: is the bits currently referred to, :x is the bits on. - ?? is the combinations, and (x) is the number of bits to encode it.
In order to get any compression, assuming you need to tell the 5bits (32), you would need to get the on bits between the 1-10 or 22-32. However there might be other things or way to use this, in much larger numbers it might be more useful, but are usually 2-3 bits away from it's middle ground.

full ref 4-64 bits.

Era