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A261489
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Number of partitions of subsets of {1,...,n}, where consecutive integers and the elements in {1, n} are required to be in different parts.
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5
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1, 2, 4, 8, 25, 82, 313, 1318, 6098, 30603, 165282, 954065, 5853242, 37987146, 259751877, 1864926846, 14016442573, 109985575616, 898948324164, 7637000950875, 67310106587314, 614420757079213, 5799709014601124, 56530981389520624, 568255134674637557
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OFFSET
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0,2
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LINKS
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EXAMPLE
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a(3) = 8: {}, 1, 2, 3, 1|2, 1|3, 2|3, 1|2|3.
a(4) = 25: {}, 1, 2, 3, 4, 1|2, 1|3, 13, 1|4, 2|3, 2|4, 24, 3|4, 1|2|3, 13|2, 1|2|4, 1|24, 1|3|4, 13|4, 2|3|4, 24|3, 1|2|3|4, 13|2|4, 1|3|24, 13|24.
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MAPLE
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g:= proc(n, l, t, f) option remember; `if`(n=0, 1,
add(`if`(l>0 and j=l or f=1 and n=1 and j=1, 0,
g(n-1, j, t+`if`(j=t, 1, 0), f)), j=0..t))
end:
a:= n-> `if`(n=0, 1, g(n-1, 0, 1, 0)+g(n-1, 1, 2, 1)):
seq(a(n), n=0..25);
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MATHEMATICA
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g[n_, l_, t_, f_] := g[n, l, t, f] = If[n==0, 1, Sum[If[l>0 && j==l || f==1 && n==1 && j==1, 0, g[n-1, j, t+If[j==t, 1, 0], f]], {j, 0, t}]]; a[n_] := If[n==0, 1, g[n-1, 0, 1, 0]+g[n-1, 1, 2, 1]]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 02 2017, translated from Maple *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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