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A328806
Row lengths of A276427: largest k such that a partition of n has k-1 distinct parts i of multiplicity i.
2
1, 2, 1, 2, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7
OFFSET
0,2
COMMENTS
Columns of A276427 are numbered starting with 0, so the row length is one more than the index of the last column.
EXAMPLE
For n = 0, the empty partition [] has 0 parts i with multiplicity i, so a(0) = 1.
For n = 1, the partition [1] has one part i with multiplicity i, whence a(1) = 2.
For n = 2, both partitions [1,1] and [2] have 0 parts i with multiplicity i, so a(2) = 1.
For n = 3, the partition [1,2] has one part i with multiplicity i, hence a(3) = 2.
For n = 4, the partitions [1,3] and [2,2] have one part i with multiplicity i, so a(4) = 2.
For n = 5, the partition [1,2,2] has 2 parts i with multiplicity i, hence a(5) = 3.
The smallest partition with k-1 = 3 parts i with multiplicity i is [1,2,2,3,3,3], for n = 14, whence a(14) = 4.
PROG
(PARI) a(n)=#A276427_row(n)
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Oct 27 2019
EXTENSIONS
More terms from Alois P. Heinz, Oct 28 2019
STATUS
approved