A320203 Number of sets of nonempty words with a total of n letters over binary alphabet such that all letters occur at least once in the set.

3, 12, 38, 110, 302, 806, 2109, 5450, 13917, 35224, 88464, 220608, 546734, 1347290, 3302716, 8057268, 19568800, 47329156, 114025658, 273709580, 654765164, 1561257760, 3711372761, 8797021430, 20794198251, 49024480496, 115292809466, 270495295124, 633186396954

Offset

2,1

Links

Alois P. Heinz, Table of n, a(n) for n = 2..1000

Example

a(2) = 3: {ab}, {ba}, {a,b}.
a(3) = 12: {aab}, {aba}, {abb}, {baa}, {bab}, {bba}, {a,ab}, {a,ba}, {a,bb}, {aa,b}, {ab,b}, {b,ba}.
a(4) = 38: {aaab}, {aaba}, {aabb}, {abaa}, {abab}, {abba}, {abbb}, {baaa}, {baab}, {baba}, {babb}, {bbaa}, {bbab}, {bbba}, {a,aab}, {a,aba}, {a,abb}, {a,baa}, {a,bab}, {a,bba}, {a,bbb}, {aa,ab}, {aa,ba}, {aa,bb}, {aaa,b}, {aab,b}, {ab,ba}, {ab,bb}, {aba,b}, {abb,b}, {b,baa}, {b,bab}, {b,bba}, {ba,bb}, {a,aa,b}, {a,ab,b}, {a,b,ba}, {a,b,bb}.

Maple

h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(h(n-i*j, i-1, k)*binomial(k^i, j), j=0..n/i)))
    end:
a:= n-> (k-> add((-1)^i*binomial(k, i)*h(n$2, k-i), i=0..k))(2):
seq(a(n), n=2..35);

Crossrefs

Column k=2 of A319501.

Sequence in context: A368097 A008907 A048246 * A217093 A278639 A350787

Adjacent sequences: A320200 A320201 A320202 * A320204 A320205 A320206

Keyword

nonn

Author

Alois P. Heinz, Oct 07 2018

Status

approved