A367450 Number of partitions of [n] whose sum of block maxima equals twice the sum of block minima.

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

Links

Table of n, a(n) for n=0..21.

Wikipedia, Partition of a set

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

Cf. A000110, A368338.

Sequence in context: A124005 A149418 A149419 * A151469 A268408 A092576

Adjacent sequences: A367447 A367448 A367449 * A367451 A367452 A367453

Keyword

nonn,more

Author

Alois P. Heinz, Dec 15 2023

Status

approved