OFFSET
1,4
COMMENTS
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..400
EXAMPLE
row 2: 1
row 3: 1 ... 1
row 4: 2 ... 1 ... 1
row 5: 1 ... 3 ... 1 ... 1
row 6: 3 ... 3 ... 2 ... 1 ... 1
row 7: 1 ... 6 ... 3 ... 2 ... 1 ... 1
row 8: 3 ... 6 ... 6 ... 2 ... 2 ... 1 ... 1
row 9: 2 ... 10 .. 6 ... 5 ... 2 ... 2 ... 1 ... 1
Let m = max(x(j) - x(j-1)); then for row 5, the 1 partition with m = 0 is 11111; the 3 partitions with m = 1 are 32, 221, 2111; the 1 partition with m = 2 is 311, and the 1 partition with m = 3 is 41.
MATHEMATICA
z = 25; p[n_, k_] := p[n, k] = IntegerPartitions[n][[k]]; m[n_, k_] := m[n, k] = Max[-Differences[p[n, k]]]; c[n_] := Table[m[n, h], {h, 1, PartitionsP[n]}]; v = Table[Count[c[n], h], {n, 2, z}, {h, 0, n - 2}]; Flatten[v]
TableForm[v]
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Mar 03 2014
STATUS
approved