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A244174 Number of compositions of 3n in which the minimal multiplicity of parts equals n. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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, A242451, A245732.

Sequence in context: A037127 A105795 A322459 * A148678 A148679 A148680

Adjacent sequences:  A244171 A244172 A244173 * A244175 A244176 A244177

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 21 2014

STATUS

approved

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Last modified December 3 20:25 EST 2021. Contains 349468 sequences. (Running on oeis4.)