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A367450
Number of partitions of [n] whose sum of block maxima equals twice the sum of block minima.
1
1, 0, 1, 0, 1, 4, 12, 55, 198, 979, 4700, 22288, 131612, 754614, 4833776, 32539094, 225628769, 1675660796, 12676652631, 100996809180, 830086817650, 7065404491242
OFFSET
0,6
EXAMPLE
a(0) = 1: the empty partition.
a(2) = 1: 12.
a(4) = 1: 134|2.
a(5) = 4: 1245|3, 1|2345, 14|25|3, 15|24|3.
a(6) = 12: 12356|4, 12|3456, 13|25|46, 13|26|45, 15|23|46, 16|23|45, 14|2|356, 1|245|36, 1|246|35, 156|2|34, 1|25|346, 1|26|345.
MAPLE
b:= proc(n, m, s) option remember;
`if`(n=0, `if`(add(i, i=m)*2=s, 1, 0),
add(b(n-1, subs(j=n, m), s), j=m)+
b(n-1, {m[], n}, s+n))
end:
a:= n-> b(n, {}, 0):
seq(a(n), n=0..15);
CROSSREFS
Sequence in context: A124005 A149418 A149419 * A151469 A268408 A092576
KEYWORD
nonn,more
AUTHOR
Alois P. Heinz, Dec 15 2023
STATUS
approved