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A372542
Total number of modes in all partitions of n.
3
0, 1, 2, 4, 6, 9, 16, 20, 30, 42, 61, 76, 112, 138, 189, 248, 325, 407, 539, 667, 865, 1083, 1369, 1690, 2140, 2624, 3268, 4009, 4954, 6022, 7417, 8968, 10946, 13218, 16023, 19256, 23264, 27819, 33415, 39873, 47682, 56654, 67527, 79962, 94909, 112130, 132578
OFFSET
0,3
COMMENTS
Each element of a partition with maximal multiplicity is a mode of this partition.
LINKS
FORMULA
a(n) = Sum_{k=0..A003056(n)} k * A362614(n,k).
EXAMPLE
a(5) = 9 = 1 + 2 + 2 + 1 + 1 + 1 + 1: 5, 32, 41, 221, 311, 2111, 11111.
MAPLE
b:= proc(n, i, m, t) option remember; `if`(n=0, t, `if`(i<1, 0, add(
b(n-i*j, i-1, max(j, m), `if`(j>m, 1, `if`(j=m, t+1, t))), j=0..n/i)))
end:
a:= n-> b(n$2, 0$2):
seq(a(n), n=0..46);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 05 2024
STATUS
approved