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 A240085 Number of compositions of n in which no part is unique (every part appears at least twice). 7
 1, 0, 1, 1, 2, 1, 9, 11, 34, 53, 108, 169, 400, 680, 1530, 2984, 6362, 12498, 25766, 50093, 102126, 199309, 400288, 788227, 1581584, 3135117, 6286310, 12532861, 25121292, 50184582, 100627207, 201208477, 403170900, 806534560, 1615151111, 3231224804, 6467909442 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 REFERENCES S. Heubach and T. Mansour, Combinatorics of Compositions and Words, Chapman and Hall, 2009. LINKS Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..2100 (first 500 terms from Alois P. Heinz) Vaclav Kotesovec, Graph a(n)/2^n EXAMPLE a(6) = 9 because we have: 3+3, 2+2+2, 2+2+1+1, 2+1+2+1, 2+1+1+2, 1+2+2+1, 1+2+1+2, 1+1+2+2, 1+1+1+1+1+1. MAPLE b:= proc(n, i, t) option remember; `if`(n=0, t!, `if`(i<1, 0,       b(n, i-1, t) +add(b(n-i*j, i-1, t+j)/j!, j=2..n/i)))     end: a:= n-> b(n\$2, 0): seq(a(n), n=0..40);  # Alois P. Heinz, Mar 31 2014 MATHEMATICA Table[Length[Level[Map[Permutations, Select[IntegerPartitions[n], Apply[And, Table[Count[#, #[[i]]]>1, {i, 1, Length[#]}]]&]], {2}]], {n, 0, 20}] (* Second program: *) b[n_, i_, t_] := b[n, i, t] = If[n == 0, t!, If[i < 1, 0, b[n, i - 1, t] + Sum[b[n - i*j, i - 1, t + j]/j!, {j, 2, n/i}]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Aug 29 2016, after Alois P. Heinz *) CROSSREFS Cf. A007690. Sequence in context: A295851 A192324 A063579 * A078623 A198204 A099599 Adjacent sequences:  A240082 A240083 A240084 * A240086 A240087 A240088 KEYWORD nonn AUTHOR Geoffrey Critzer, Mar 31 2014 EXTENSIONS More terms from Alois P. Heinz, Mar 31 2014 STATUS approved

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Last modified April 1 02:24 EDT 2020. Contains 333153 sequences. (Running on oeis4.)