A243120 Number of compositions of n in which the maximal multiplicity of parts equals 3.

1, 0, 4, 5, 18, 34, 59, 132, 272, 519, 966, 1746, 3487, 5986, 10570, 19701, 34444, 59250, 101155, 180588, 302788, 515205, 841042, 1449392, 2420163, 3959442, 6472636, 10656987, 17332640, 28234296, 45337971, 72306544, 117761744, 185704091, 295918788, 466574348

Offset

3,3

Links

Alois P. Heinz, Table of n, a(n) for n = 3..1000

Formula

a(n) = A232464(n) - A232432(n) = A243081(n,3) - A243081(n,2).

Maple

b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
      add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
    end:
a:= n-> b(n$2, 0, 3) -b(n$2, 0, 2):
seq(a(n), n=3..50);

Crossrefs

Column k=3 of A242447.

Sequence in context: A026902 A026755 A368029 * A317378 A338866 A308485

Adjacent sequences: A243117 A243118 A243119 * A243121 A243122 A243123

Keyword

nonn

Author

Alois P. Heinz, May 29 2014

Status

approved