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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.)