A367450 - OEIS

%I #24 Dec 21 2023 21:52:47

%S 1,0,1,0,1,4,12,55,198,979,4700,22288,131612,754614,4833776,32539094,

%T 225628769,1675660796,12676652631,100996809180,830086817650,

%U 7065404491242

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%e a(0) = 1: the empty partition.

%e a(2) = 1: 12.

%e a(4) = 1: 134|2.

%e a(5) = 4: 1245|3, 1|2345, 14|25|3, 15|24|3.

%e 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.

%p b:= proc(n, m, s) option remember;

%p      `if`(n=0, `if`(add(i, i=m)*2=s, 1, 0),

%p       add(b(n-1, subs(j=n, m), s), j=m)+

%p           b(n-1, {m[], n}, s+n))

%p     end:

%p a:= n-> b(n, {}, 0):

%p seq(a(n), n=0..15);

%Y Cf. A000110, A368338.

%K nonn,more

%O 0,6

%A _Alois P. Heinz_, Dec 15 2023