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A364808
a(n) = sum of minimal runlengths of all the partitions of n.
2
1, 3, 5, 9, 11, 20, 22, 36, 44, 63, 74, 114, 128, 180, 224, 298, 355, 485, 573, 760, 922, 1174, 1419, 1836, 2189, 2756, 3341, 4160, 4988, 6217, 7412, 9131, 10941, 13326, 15916, 19379, 22988, 27770, 33017, 39662, 46919, 56223, 66308, 79047, 93187, 110512
OFFSET
1,2
LINKS
EXAMPLE
The partitions of 4 are [4], [3,1], [2,2], [2,1,1], [1,1,1,1], with runlengths {1}, {1,1}, {2}, {1,2}, {4} having minima 1, 1, 2, 1, 4, with sum 9, so that a(4) = 9.
MAPLE
b:= proc(n, i, m) option remember; `if`(n=0, m, `if`(i=1, min(m, n),
add(b(n-i*j, i-1, `if`(j=0, m, min(m, j))), j=0..n/i)))
end:
a:= n-> b(n$3):
seq(a(n), n=1..50); # Alois P. Heinz, Sep 17 2023
MATHEMATICA
m[n_] := m[n] = Map[Split, IntegerPartitions[n]]
t[n_] := t[n] = Table[Map[Length, m[n][[k]]], {k, 1, PartitionsP[n]}]
Table[Total[Map[Min, t[n]]], {n, 1, 47}]
PROG
(Python)
from sympy.utilities.iterables import partitions
def A364808(n): return sum(min(p.values()) for p in partitions(n)) # Chai Wah Wu, Sep 17 2023
CROSSREFS
Cf. A000041, A264397 (sum of maximal runlengths).
Sequence in context: A034760 A070639 A078392 * A187753 A339638 A231716
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 10 2023
STATUS
approved