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Pancake sorting
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==Related integer sequences== :{| class="wikitable" align="center" style="float: center; text-align: right;" |+ Number of stacks of given height {{math|''n''}} that require unique flips {{math|''k''}} to get sorted ! rowspan=2 | Height<br />{{math|''n''}} !! colspan=16 | {{math|''k''}} |- ! width="65px" | 0 !! width="65px" | 1 !! width="65px" | 2 !! width="65px" | 3 !! width="65px" | 4 !! width="65px" | 5 !! width="65px" | 6 !! width="65px" | 7 ! width="65px" | 8 !! width="65px" | 9 !! width="65px" | 10 !! width="65px" | 11 !! width="65px" | 12 !! width="65px" | 13 !! width="65px" | 14 !! width="65px"|15 |- ! 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 || |- ! 13 | 1 || 12 || 132 || 1451 || 14556 || 130096 || 1030505 || 7046318 || 40309555 || 184992275 || 639783475 || 1525125357 || 2183056566 || 1458653648 || 186874852 || 2001 |} Sequences from [[On-Line Encyclopedia of Integer Sequences|The Online Encyclopedia of Integer Sequences]]: * {{OEIS2C|A058986}} β maximum number of flips * {{OEIS2C|A067607}} β number of stacks requiring the maximum number of flips (above) * {{OEIS2C|A078941}} β maximum number of flips for a "burnt" stack * {{OEIS2C|A078942}} β the number of flips for a sorted "burnt-side-on-top" stack * {{OEIS2C|A092113}} β the above triangle, read by rows
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