A368501 Number of compositions (ordered partitions) of n into distinct parts not greater than n/2.

1, 0, 0, 0, 0, 0, 6, 0, 6, 6, 36, 30, 66, 60, 120, 234, 318, 432, 666, 894, 1272, 2226, 2772, 3960, 5496, 7524, 10068, 13776, 22488, 27756, 39162, 51264, 70398, 91386, 124152, 158574, 247554, 301656, 416748, 537690, 730854, 929196, 1248798, 1576014, 2078328, 2956110

Offset

0,7

Links

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Index entries for sequences related to compositions

Formula

a(n) = Sum_{k=1..floor(n/2)} A072575(n,k) for n>=1. - Alois P. Heinz, Dec 31 2023

Example

a(6) = 6 because we have [1,2,3], [1,3,2], [2,1,3], [2,3,1], [3,1,2] and [3,2,1].

Maple

b:= proc(n, i, p) option remember; `if`(i*(i+1)/2<n, 0,
     `if`(n=0, p!, b(n, i-1, p)+b(n-i, min(n-i, i-1), p+1)))
    end:
a:= n-> b(n, iquo(n, 2), 0):
seq(a(n), n=0..45);  # Alois P. Heinz, Dec 28 2023

Mathematica

Table[Sum[Count[IntegerPartitions[n, {k}], _?(And[UnsameQ @@ #, AllTrue[#, # <= n/2 &]] &)] k!, {k, 0, n}], {n, 0, 45}]

Crossrefs

Cf. A008289, A032020, A072575, A110618, A258259, A368484.

Sequence in context: A004016 A093577 A065442 * A198752 A141462 A354330

Adjacent sequences: A368498 A368499 A368500 * A368502 A368503 A368504

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 27 2023

Status

approved