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