|
|
A239954
|
|
Number of partitions p of n such that (number of distinct parts of p) < max(p) - min(p).
|
|
6
|
|
|
0, 0, 0, 0, 0, 1, 2, 4, 6, 12, 17, 26, 38, 54, 76, 107, 142, 192, 259, 337, 443, 577, 743, 948, 1213, 1532, 1935, 2427, 3031, 3765, 4681, 5762, 7097, 8704, 10644, 12966, 15775, 19104, 23115, 27874, 33546, 40257, 48259, 57656, 68809, 81929, 97378, 115495
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,7
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(7) counts these 4 partitions: 61, 52, 511, 1111111.
|
|
MATHEMATICA
|
z = 60; d[p_] := d[p] = Length[DeleteDuplicates[p]]; f[p_] := f[p] = Max[p] - Min[p]; g[n_] := g[n] = IntegerPartitions[n];
Table[Count[g[n], p_ /; d[p] < f[p]], {n, 0, z}] (*A239954*)
Table[Count[g[n], p_ /; d[p] <= f[p]], {n, 0, z}] (*A239955*)
Table[Count[g[n], p_ /; d[p] == f[p]], {n, 0, z}] (*A239956*)
Table[Count[g[n], p_ /; d[p] > f[p]], {n, 0, z}] (*A034296*)
Table[Count[g[n], p_ /; d[p] >= f[p]], {n, 0, z}] (*A239958*)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|