A244174 Number of compositions of 3n in which the minimal multiplicity of parts equals n.

1, 3, 7, 21, 71, 253, 925, 3433, 12871, 48621, 184757, 705433, 2704157, 10400601, 40116601, 155117521, 601080391, 2333606221, 9075135301, 35345263801, 137846528821, 538257874441, 2104098963721, 8233430727601, 32247603683101, 126410606437753, 495918532948105

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) = A242451(3n,n).

Recurrence: see Maple program.

For n>0, a(n) = 1 + C(2n,n) = 1 + A000984(n). - Vaclav Kotesovec, Jun 21 2014

G.f.: 1/(sqrt(1-4*x)) + x/(1-x). - Alois P. Heinz, Jun 22 2014

a(n) = A245732(2n,n). - Alois P. Heinz, Jul 30 2014

a(n) = A065567(2n,n) for n>=1. - Alois P. Heinz, Sep 05 2023

Example

a(2) = 7: [1,1,2,2], [1,2,1,2], [1,2,2,1], [2,1,1,2], [2,1,2,1], [2,2,1,1], [3,3].

Maple

a:= proc(n) option remember;
      `if`(n<3, 2^(n+1)-1, ((15*n^2-31*n+12) *a(n-1)
       -2*(3*n-2)*(2*n-3) *a(n-2)) / ((3*n-5)*n))
    end:
seq(a(n), n=0..30);

Mathematica

a[n_] := a[n] = If[n < 3, 2^(n+1) - 1, ((15*n^2 - 31*n + 12)*a[n-1] - 2*(3*n - 2)*(2*n - 3)*a[n-2])/((3*n - 5)*n)]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 07 2014, after Alois P. Heinz *)

Prog

(Sage)
A244174 = lambda m: SetPartitions(2*m, [2*m]).cardinality()+2*SetPartitions(2*m, [m, m]).cardinality()
[1] + [A244174(m) for m in (1..26)] # Peter Luschny, Aug 02 2015

Crossrefs

Cf. A000984, A007318, A065567, A242451, A245732.

Sequence in context: A037127 A105795 A322459 * A372649 A148678 A148679

Adjacent sequences: A244171 A244172 A244173 * A244175 A244176 A244177

Keyword

nonn

Author

Alois P. Heinz, Jun 21 2014

Status

approved