A single Berge k-move is denoted as { j i }, in which case, the pieces in the positions
i,i+1,...,i+k-1 are moved to the vacant holes j,j+1,...,j+k-1.  Successive moves are concatenated
as { j i } U { l k }, which means perform { j i } followed by { l k }. Often a move fills an
empty hole created as an effect of the previous move, the resulting notation { j k } U { k i }
is abbreviated as { j k i }, and is extended to more than two such moves as well.

S[5, 2]: { 6 2 5 1 }
S[6, 2]: { 7 4 1 } U { 9 3 }
S[7, 2]: { 8 5 2 8 1 }
S[8, 2]: { 9 2 5 8 1 }
S[9, 2]: { 10 1 } U { 12 4 7 11 3 }
S[10, 2]: { 11 2 7 4 10 1 }
S[11, 2]: { 12 1 } U { 14 4 9 6 13 3 }
S[12, 2]: { 13 2 5 10 6 12 1 }
S[13, 2]: { 14 1 } U { 16 4 7 12 8 15 3 }
S[14, 2]: { 15 2 9 6 11 5 14 1 }
S[15, 2]: { 16 1 } U { 18 4 11 8 13 7 17 3 }
S[16, 2]: { 17 2 5 12 9 13 6 16 1 }
S[17, 2]: { 18 1 } U { 20 4 7 14 11 15 8 19 3 }
S[18, 2]: { 19 2 11 6 15 8 14 5 18 1 }
S[19, 2]: { 20 1 } U { 22 4 13 8 17 10 16 7 21 3 }
S[20, 2]: { 21 2 5 14 9 18 10 15 6 20 1 }
S[21, 2]: { 22 1 } U { 24 4 7 16 11 20 12 17 8 23 3 }
S[22, 2]: { 23 2 13 6 19 10 15 9 18 5 22 1 }
S[23, 2]: { 24 1 } U { 26 4 15 8 21 12 17 11 20 7 25 3 }
S[24, 2]: { 25 2 5 16 9 20 13 21 10 17 6 24 1 }
S[25, 2]: { 26 1 } U { 28 4 7 18 11 22 15 23 12 19 8 27 3 }
S[26, 2]: { 27 2 15 6 23 10 19 12 18 9 22 5 26 1 }
S[27, 2]: { 28 1 } U { 30 4 17 8 25 12 21 14 20 11 24 7 29 3 }
S[28, 2]: { 29 2 5 18 9 22 13 26 14 23 10 19 6 28 1 }
S[29, 2]: { 30 1 } U { 32 4 7 20 11 24 15 28 16 25 12 21 8 31 3 }
S[30, 2]: { 31 2 17 6 27 10 23 14 19 13 22 9 26 5 30 1 }
S[31, 2]: { 32 1 } U { 34 4 19 8 29 12 25 16 21 15 24 11 28 7 33 3 }
S[32, 2]: { 33 2 5 20 9 24 13 28 17 29 14 25 10 21 6 32 1 }
S[33, 2]: { 34 1 } U { 36 4 7 22 11 26 15 30 19 31 16 27 12 23 8 35 3 }
S[34, 2]: { 35 2 19 6 31 10 27 14 23 16 22 13 26 9 30 5 34 1 }
S[35, 2]: { 36 1 } U { 38 4 21 8 33 12 29 16 25 18 24 15 28 11 32 7 37 3 }
S[36, 2]: { 37 2 5 22 9 26 13 30 17 34 18 31 14 27 10 23 6 36 1 }
S[37, 2]: { 38 1 } U { 40 4 7 24 11 28 15 32 19 36 20 33 16 29 12 25 8 39 3 }
S[38, 2]: { 39 2 21 6 35 10 31 14 27 18 23 17 26 13 30 9 34 5 38 1 }
S[39, 2]: { 40 1 } U { 42 4 23 8 37 12 33 16 29 20 25 19 28 15 32 11 36 7 41 3 }
S[40, 2]: { 41 2 5 24 9 28 13 32 17 36 21 37 18 33 14 29 10 25 6 40 1 }
S[41, 2]: { 42 1 } U { 44 4 7 26 11 30 15 34 19 38 23 39 20 35 16 31 12 27 8 43 3 }
S[42, 2]: { 43 2 23 6 39 10 35 14 31 18 27 20 26 17 30 13 34 9 38 5 42 1 }
S[43, 2]: { 44 1 } U { 46 4 25 8 41 12 37 16 33 20 29 22 28 19 32 15 36 11 40 7 45 3 }
S[44, 2]: { 45 2 5 26 9 30 13 34 17 38 21 42 22 39 18 35 14 31 10 27 6 44 1 }
S[45, 2]: { 46 1 } U { 48 4 7 28 11 32 15 36 19 40 23 44 24 41 20 37 16 33 12 29 8 47 3 }
S[46, 2]: { 47 2 25 6 43 10 39 14 35 18 31 22 27 21 30 17 34 13 38 9 42 5 46 1 }
S[47, 2]: { 48 1 } U { 50 4 27 8 45 12 41 16 37 20 33 24 29 23 32 19 36 15 40 11 44 7 49 3 }
S[48, 2]: { 49 2 5 28 9 32 13 36 17 40 21 44 25 45 22 41 18 37 14 33 10 29 6 48 1 }
S[49, 2]: { 50 1 } U { 52 4 7 30 11 34 15 38 19 42 23 46 27 47 24 43 20 39 16 35 12 31 8 51 3 }
S[50, 2]: { 51 2 27 6 47 10 43 14 39 18 35 22 31 24 30 21 34 17 38 13 42 9 46 5 50 1 }