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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Feb 02 2017, translated from Maple *)

CROSSREFS

Cf. A247100, A261134, A261041, A261492.

Sequence in context: A134455 A191700 A000643 * A286936 A196265 A112285

Adjacent sequences:  A261486 A261487 A261488 * A261490 A261491 A261492

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 21 2015

STATUS

approved

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Last modified February 24 06:13 EST 2018. Contains 299597 sequences. (Running on oeis4.)