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, 3]: { 6 2 5 1 }
S[6, 3]: { 7 2 6 1 }
S[7, 3]: { -2 4 -1 3 -2 }
S[8, 3]: { 9 2 7 3 9 }
S[9, 3]: { 10 4 9 3 8 1 }
S[10, 3]: { 11 4 10 3 8 1 }
S[11, 3]: { -2 8 1 7 0 5 -2 }
S[12, 3]: { 13 2 5 11 3 12 6 1 }
S[13, 3]: { 14 6 13 5 12 3 10 1 }
S[14, 3]: { 15 6 14 5 12 3 10 1 }
S[15, 3]: { -2 12 3 11 2 9 0 7 -2 }
S[16, 3]: { 17 2 7 4 9 15 11 3 7 17 }
S[17, 3]: { 18 8 17 7 16 5 14 3 12 1 }
S[18, 3]: { 19 8 18 7 16 5 14 3 12 1 }
S[19, 3]: { -2 16 5 15 4 13 2 11 0 9 -2 }
S[20, 3]: { 21 2 7 12 17 } U { 24 13 22 6 1 } U { 17 8 24 }
S[21, 3]: { 22 10 21 9 20 7 18 5 16 3 14 1 }
S[22, 3]: { 23 10 22 9 20 7 18 5 16 3 14 1 }
S[23, 3]: { -2 20 7 19 6 17 4 15 2 13 0 11 -2 }
S[24, 3]: { 25 6 13 18 } U { -2 4 8 24 14 22 } U { 18 -1 12 3 25 }
S[25, 3]: { 26 12 25 11 24 9 22 7 20 5 18 3 16 1 }
S[26, 3]: { 27 12 26 11 24 9 22 7 20 5 18 3 16 1 }
S[27, 3]: { -2 24 9 23 8 21 6 19 4 17 2 15 0 13 -2 }
S[28, 3]: { 29 2 7 16 23 12 } U { 32 17 21 25 30 6 1 } U { 12 23 8 32 }
S[29, 3]: { 30 14 29 13 28 11 26 9 24 7 22 5 20 3 18 1 }
S[30, 3]: { 31 14 30 13 28 11 26 9 24 7 22 5 20 3 18 1 }
S[31, 3]: { -2 28 11 27 10 25 8 23 6 21 4 19 2 17 0 15 -2 }
S[32, 3]: { 33 2 7 12 17 24 } U { 36 6 31 13 29 19 1 } U { 24 11 28 18 35 4 }
S[33, 3]: { 34 16 33 15 32 13 30 11 28 9 26 7 24 5 22 3 20 1 }
S[34, 3]: { 35 16 34 15 32 13 30 11 28 9 26 7 24 5 22 3 20 1 }
S[35, 3]: { -2 32 13 31 12 29 10 27 8 25 6 23 4 21 2 19 0 17 -2 }
S[36, 3]: { 37 2 7 12 17 32 23 28 } U { 40 6 18 13 24 33 1 } U { 28 11 35 19 39 4 }
S[37, 3]: { 38 18 37 17 36 15 34 13 32 11 30 9 28 7 26 5 24 3 22 1 }
S[38, 3]: { 39 18 38 17 36 15 34 13 32 11 30 9 28 7 26 5 24 3 22 1 }
S[39, 3]: { -2 36 15 35 14 33 12 31 10 29 8 27 6 25 4 23 2 21 0 19 -2 }
S[40, 3]: { 41 2 7 12 17 26 33 } U { 44 13 28 19 42 6 1 } U { 33 27 37 8 25 15 29 20 44 }
S[41, 3]: { 42 20 41 19 40 17 38 15 36 13 34 11 32 9 30 7 28 5 26 3 24 1 }
S[42, 3]: { 43 20 42 19 40 17 38 15 36 13 34 11 32 9 30 7 28 5 26 3 24 1 }
S[43, 3]: { -2 40 17 39 16 37 14 35 12 33 10 31 8 29 6 27 4 25 2 23 0 21 -2 }
S[44, 3]: { 45 2 7 12 17 22 29 36 41 } U { 48 13 21 37 27 31 46 6 1 } U { 41 8 29 15 35 19 48 }
S[45, 3]: { 46 22 45 21 44 19 42 17 40 15 38 13 36 11 34 9 32 7 30 5 28 3 26 1 }
S[46, 3]: { 47 22 46 21 44 19 42 17 40 15 38 13 36 11 34 9 32 7 30 5 28 3 26 1 }
S[47, 3]: { -2 44 19 43 18 41 16 39 14 37 12 35 10 33 8 31 6 29 4 27 2 25 0 23 -2 }
S[48, 3]: { 49 2 7 12 17 22 27 36 41 } U { 52 6 18 26 47 13 45 37 1 } U { 41 32 11 39 20 43 24 51 4 }
S[49, 3]: { 50 24 49 23 48 21 46 19 44 17 42 15 40 13 38 11 36 9 34 7 32 5 30 3 28 1 }
S[50, 3]: { 51 24 50 23 48 21 46 19 44 17 42 15 40 13 38 11 36 9 34 7 32 5 30 3 28 1 }