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A325512
Number of distinct nonzero numbers of partitions of n counted by length.
4
1, 1, 1, 1, 2, 2, 3, 4, 5, 7, 7, 7, 10, 9, 10, 12, 14, 15, 16, 16, 18, 19, 19, 20, 22, 23, 23, 25, 26, 27, 27, 28, 30, 31, 31, 33, 34, 35, 36, 37, 38, 39, 40, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 56, 58, 60, 61, 62, 63, 64, 65, 65
OFFSET
0,5
COMMENTS
Also the number of distinct nonzero entries in row n of A008284.
EXAMPLE
Row n = 9 of A008284 is (1, 4, 7, 6, 5, 3, 2, 1, 1), which has union {1,2,3,4,5,6,7}, so a(9) = 7.
MAPLE
b:= proc(n, i) option remember; `if`(n=0 or i=1, x^n,
b(n, i-1)+expand(x*b(n-i, min(n-i, i))))
end:
a:= n-> nops({coeffs(b(n$2))}):
seq(a(n), n=0..90); # Alois P. Heinz, Feb 23 2024
MATHEMATICA
Table[Length[Union[Table[Length[IntegerPartitions[n, {k}]], {k, n}]]], {n, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 07 2019
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Feb 23 2024
STATUS
approved