A336032 Number of compositions of n such that the set of parts and the set of multiplicities of parts are disjoint.

1, 0, 2, 2, 2, 4, 6, 6, 14, 34, 79, 159, 227, 429, 727, 1146, 1999, 3238, 5018, 8976, 14977, 24768, 38400, 70678, 152535, 295493, 617675, 1404099, 3023086, 6685876, 14230031, 30218806, 62175519, 127820798, 257285277, 516574751, 1021334631, 2009999405, 3917878730

Offset

0,3

Links

Table of n, a(n) for n=0..38.

Maple

b:= proc(n, i, p, f, g) option remember; `if`(f intersect g<>{}, 0,
      `if`(n=0, p!, `if`(i<1, 0, add(b(n-i*j, i-1, p+j, `if`(j=0,
       f, {f[], i}), `if`(j=0, g, {g[], j}))/j!, j=0..n/i))))
    end:
a:= n-> b(n$2, 0, {}$2):
seq(a(n), n=0..32);

Mathematica

b[n_, i_, p_, f_, g_] := b[n, i, p, f, g] = If[f ~Intersection~ g != {}, 0,
     If[n == 0, p!, If[i < 1, 0, Sum[b[n - i*j, i - 1, p + j,
     If[j == 0, f, Union@Append[f, i]],
     If[j == 0, g, Union@Append[g, j]]]/j!, {j, 0, n/i}]]]];
a[n_] := b[n, n, 0, {}, {}];
Table[a[n], {n, 0, 38}] (* Jean-François Alcover, Apr 13 2022, after Alois P. Heinz *)

Crossrefs

Cf. A114639, A336031.

Sequence in context: A002722 A261610 A265251 * A093393 A341095 A090858

Adjacent sequences: A336029 A336030 A336031 * A336033 A336034 A336035

Keyword

nonn

Author

Alois P. Heinz, Jul 07 2020

Status

approved