a(n,k) tabf head (staircase) for A049085 Maximal part of the partitions of n ordered according to the Abramowitz-Stegun table with increasing number of parts m=1..n (ref. given in A049085, p.831-2) n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 3 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 5 4 3 3 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 6 5 4 3 4 3 2 3 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 7 6 5 4 5 4 3 3 4 3 2 3 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 7 6 5 4 6 5 4 4 3 5 4 3 3 2 4 3 2 3 2 2 1 0 0 0 0 0 0 0 0 9 9 8 7 6 5 7 6 5 4 5 4 3 6 5 4 4 3 3 5 4 3 3 2 4 3 2 3 2 2 1 . . . n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 For n=10 the 42 entries are: [10, 9, 8, 7, 6, 5, 8, 7, 6, 5, 6, 5, 4, 4, 7, 6, 5, 4, 5, 4, 3, 4, 3, 6, 5, 4, 4, 3, 3, 2, 5, 4, 3, 3, 2, 4, 3, 2, 3, 2, 2, 1] ################################################## Abramowitz -Stegun checks ################################################## For n=11 the 56 entries are: [11, 10, 9, 8, 7, 6, 9, 8, 7, 6, 5, 7, 6, 5, 5, 4, 8, 7, 6, 5, 6, 5, 4, 5, 4, 4, 3, 7, 6, 5, 4, 5, 4, 3, 4, 3, 3, 6, 5, 4, 4, 3, 3, 2, 5, 4, 3, 3, 2, 4, 3, 2, 3, 2, 2, 1] For n=12 the 77 entries are: [12, 11, 10, 9, 8, 7, 6, 10, 9, 8, 7, 6, 8, 7, 6, 5, 6, 5, 4, 9, 8, 7, 6, 5, 7, 6, 6, 5, 5, 4, 5, 4, 4, 3, 8, 7, 6, 5, 6, 5, 5, 4, 4, 4, 4, 3, 3, 7, 6, 5, 4, 5, 4, 3, 4, 3, 3, 2, 6, 5, 4, 4, 3, 3, 2, 5, 4, 3, 3, 2, 4, 3, 2, 3, 2, 2, 1] For n=13 the 101 entries are: [13, 12, 11, 10, 9, 8, 7, 11, 10, 9, 8, 7, 6, 9, 8, 7, 6, 7, 6, 5, 5, 10, 9, 8, 7, 6, 8, 7, 7, 6, 5, 6, 5, 4, 6, 5, 5, 4, 4, 9, 8, 7, 6, 5, 7, 6, 5, 4, 6, 5, 5, 5, 4, 4, 3, 4, 3, 8, 7, 6, 5, 6, 5, 5, 4, 4, 4, 4, 3, 3, 3, 7, 6, 5, 4, 5, 4, 3, 4, 3, 3, 2, 6, 5, 4, 4, 3, 3, 2, 5, 4, 3, 3, 2, 4, 3, 2, 3, 2, 2, 1] For n=14 the 135 entries are: [14, 13, 12, 11, 10, 9, 8, 7, 12, 11, 10, 9, 8, 7, 10, 9, 8, 7, 6, 8, 7, 6, 6, 5, 11, 10, 9, 8, 7, 6, 9, 8, 6, 7, 6, 5, 8, 7, 7, 6, 5, 6, 5, 5, 4, 5, 4, 10, 9, 8, 7, 6, 8, 7, 5, 6, 5, 4, 7, 6, 6, 6, 5, 5, 5, 4, 4, 4, 4, 3, 9, 8, 7, 6, 5, 7, 6, 4, 6, 5, 5, 5, 3, 5, 4, 4, 4, 4, 3, 3, 8, 7, 6, 5, 6, 5, 4, 5, 4, 4, 4, 3, 3, 3, 2, 7, 6, 5, 4, 5, 4, 3, 4, 3, 3, 2, 6, 5, 4, 4, 3, 3, 2, 5, 4, 3, 3, 2, 4, 3, 2, 3, 2, 2, 1] For n=15 the 176 entries are: [15, 14, 13, 12, 11, 10, 9, 8, 13, 12, 11, 10, 9, 8, 7, 11, 10, 9, 8, 7, 9, 8, 7, 6, 7, 6, 5, 12, 11, 10, 9, 8, 7, 10, 9, 9, 8, 7, 6, 8, 7, 6, 6, 5, 8, 7, 6, 7, 6, 5, 6, 5, 5, 4, 11, 10, 9, 8, 7, 6, 9, 8, 5, 5, 8, 7, 6, 7, 6, 7, 7, 6, 5, 6, 6, 5, 5, 4, 5, 4, 5, 4, 4, 3, 10, 9, 8, 7, 6, 8, 7, 5, 4, 7, 6, 6, 6, 6, 5, 5, 5, 4, 5, 5, 4, 4, 4, 4, 3, 3, 9, 8, 7, 6, 5, 7, 6, 5, 4, 6, 5, 5, 3, 5, 4, 4, 4, 4, 3, 3, 3, 8, 7, 6, 5, 6, 5, 4, 5, 4, 4, 4, 3, 3, 3, 2, 7, 6, 5, 4, 5, 4, 3, 4, 3, 3, 2, 6, 5, 4, 4, 3, 3, 2, 5, 4, 3, 3, 2, 4, 3, 2, 3, 2, 2, 1] ... #################################################################################################################################