The first 32 solutions for A302928:
  Maximum number of 4's possible in an infinite Minesweeper grid with n mines.
  
By Dmitry Kamenetsky, 16/04/2018


a(1-3)=0

a(4-5)=2
below is a(4)
..x4x.....
..x4x.....

a(6)=4
..x4x4x...
..x4x4x...

a(7-8)=6
below is a(7)
....x.....
...444....
..xxxxx...
...444....
....x.....

a(9)=7
....x.....
.x4444x...
.xxxxx....
..444.....
...x......

a(10)=8
..x.......
..444x4x..
.xxxxx4x..
..444.....
...x......

a(11)=10
....x..x..
...44444..
..xxxxxxx.
...44444..
...x..x...

a(12-13)=12
this is the first time that a(n)>=n
below is a(12)
...x..x...
..444444..
.xxxxxxxx.
..444444..
...x..x...

a(14)=13
.....xx...
...x444...
..4x4xx...
.x4x.44...
..4x4xx...
...x444...
.....xx...

a(15)=14
....x..x..
...444444.
..xxxxxxxx
.44444444.
xxx..x..x.

a(16)=16
..x..x..x.
.44444444.
xxxxxxxxxx
.44444444.
..x..x..x.

a(17-18)=18
this is the first time that a(n)>=n+1
below is a(17)
...x..x..x..
..444444444.
.xxxxxxxxxxx
..444444444.
...x..x..x..

a(19)=19
.....x4x....
.....x4x4x..
....4444x4..
...xxxx4x4x.
....4444x4..
.....x4x4x..
.....x4x4...
........x...

a(20)=21
.......x....
......4x4...
.....x4x4x..
....4x4.4x4.
...x4x4.4x4x
....4x4x4x4.
.....x44x4x.
......x4x4..
........x...

a(21)=22
.....x......
...x444.....
..44xxxx....
.xxx44444...
x444x..xxx..
..x444444...
...xxxxx....
....444.....
.....x......

a(22-23)=24
this is the first time that a(n)>=n+2
below is a(22)
.......x....
......444...
...x.xxxxx..
..444444444.
.xxxx.x..xxx
..444444444.
...x.xxxxx..
......444...
.......x....

a(24)=26
...x..x.......
..444444......
.xxxxxxxx.....
..4444444.....
.x..x..x.x....
..4444444.....
.xxxxxxxx.....
..444444......
...x..x.......

a(25)=28
this is the first time that a(n)>=n+3
...x..x.......
..444444......
.xxxxxxxx.....
.44444444.....
xx..x..x.x....
.44444444.....
.xxxxxxxx.....
..444444......
...x..x.......

a(26-27)=30
this is the first time that a(n)>=n+4
below is a(26)
......x..x....
.....444444...
....xxxxxxxx..
....444444444.
...x.x..x..xxx
....444444444.
....xxxxxxxx..
.....444444...
......x..x....

a(28)=31
.....x........
....4444x4x4x.
...xxxxxx4x4x.
...444444444..
..x.x..x.xxx..
...44444444...
...xxxxxx4x...
....4444x4x...
.....x........

a(29)=33
......x..x....
.....444444...
....xxxxxxxx..
...444444444x.
..xxx..x..x44.
...44444444xxx
....xxxxxxx44.
.....444444x..
......x..x....

a(30)=34
...x..........
..4444x4x4x...
.xxxxxx4x4x...
.444444444....
x.x..x.xxx....
.444444444....
.xxxxxx4x4x...
..4444x4x4x...
...x..........


a(31-32)=36
this is the first time that a(n)>=n+5
below is a(31)
..x..x..x......
.444444444.....
xxxxxxxxxxx....
.444444444.....
..x..x..x......
.444444444.....
xxxxxxxxxxx....
.444444444.....
..x..x..x......