A275521 Number of (n+floor(n/2))-block bicoverings of an n-set.

1, 0, 1, 4, 3, 40, 15, 420, 105, 5040, 945, 69300, 10395, 1081080, 135135, 18918900, 2027025, 367567200, 34459425, 7856748900, 654729075, 183324141000, 13749310575, 4638100767300, 316234143225, 126493657290000, 7905853580625, 3699939475732500, 213458046676875

Offset

0,4

Comments

There are no bicoverings of an n-set with more than n+floor(n/2) blocks.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..808

Formula

a(n) = A059443(n,n+floor(n/2)).

Example

a(2) = 1: 1|12|2.
a(3) = 4: 1|12|23|3, 1|13|2|23, 1|123|2|3, 12|13|2|3.
a(4) = 3: 1|12|2|3|34|4, 1|13|2|24|3|4, 1|14|2|23|3|4.

Maple

a:= proc(n) option remember; `if`(n<5, [1, 0, 1, 4, 3]
       [n+1], ((8*n-41)*a(n-1) +(6*n^2-12*n-12)*a(n-2)
       -(n-2)*(8*n-17)*a(n-3)) / (6*n-24))
    end:
seq(a(n), n=0..30);

Crossrefs

Right border of triangle A059443.

Bisections give: A001147, 4*A000457(n-1) (for n>0).

Sequence in context: A220363 A120078 A096201 * A025175 A248247 A016504

Adjacent sequences: A275518 A275519 A275520 * A275522 A275523 A275524

Keyword

nonn

Author

Alois P. Heinz, Jul 31 2016

Status

approved