A261489 Number of partitions of subsets of {1,...,n}, where consecutive integers and the elements in {1, n} are required to be in different parts.

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

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..250

Example

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.

Maple

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);

Mathematica

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 *)

Crossrefs

Cf. A247100, A261134, A261041, A261492.

Sequence in context: A134455 A191700 A000643 * A286936 A323948 A196265

Adjacent sequences: A261486 A261487 A261488 * A261490 A261491 A261492

Keyword

nonn

Author

Alois P. Heinz, Aug 21 2015

Status

approved