A327847 Number of colored compositions of n using all colors of a 2-set such that all parts have different color patterns and the patterns for parts i have i colors in (weakly) increasing order.

0, 0, 3, 10, 39, 100, 303, 782, 2009, 5388, 12839, 32658, 79673, 191500, 459745, 1090622, 2569597, 5932304, 13906405, 31740090, 72160311, 164296384, 369673125, 827781598, 1834885695, 4076433368, 8966677703, 19639987986, 42751905899, 92703023676, 200647122467

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..800

Example

a(3) = 10: 3aab, 3abb, 2aa1b, 2ab1a, 2ab1b, 2bb1a, 1a2ab, 1a2bb, 1b2aa, 1b2ab.

Maple

b:= proc(n, i, k, p) option remember; `if`(n=0, p!,
     `if`(i<1, 0, add(b(n-i*j, min(n-i*j, i-1), k, p+j)*
      binomial(binomial(k+i-1, i), j), j=0..n/i)))
    end:
a:= n-> (k-> add(b(n$2, i, 0)*(-1)^(k-i)*binomial(k, i), i=0..k))(2):
seq(a(n), n=0..37);

Crossrefs

Column k=2 of A327245.

Sequence in context: A103296 A259859 A298940 * A111749 A149048 A149049

Adjacent sequences: A327844 A327845 A327846 * A327848 A327849 A327850

Keyword

nonn

Author

Alois P. Heinz, Sep 27 2019

Status

approved