Pancake Sorting - Related Integer Sequences

Related Integer Sequences

Number of stacks of given height that require N flips to get sorted
Height N
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 1
2 1 1
3 1 2 2 1
4 1 3 6 11 3
5 1 4 12 35 48 20
6 1 5 20 79 199 281 133 2
7 1 6 30 149 543 1357 1903 1016 35
8 1 7 42 251 1191 4281 10561 15011 8520 455
9 1 8 56 391 2278 10666 38015 93585 132697 79379 5804
10 1 9 72 575 3963 22825 106461 377863 919365 1309756 814678 73232
11 1 10 90 809 6429 43891 252737 1174766 4126515 9981073 14250471 9123648 956354 6
12 1 11 110 1099 9883 77937 533397 3064788 14141929 49337252 118420043 169332213 111050066 13032704 167

Sequences from The Online Encyclopedia of Integer Sequences of Neil Sloane:

  •  A058986 – maximum number of flips
  •  A067607 – number of stacks requiring the maximum number of flips (above)
  •  A078941 – maximum number of flips for a "burnt" stack
  •  A078942 – the number of flips for a sorted "burnt-side-on-top" stack
  •  A092113 – the above triangle, read by rows

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