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A261041 Number of partitions of subsets of {1,...,n}, where consecutive integers are required to be in different parts. 5
1, 2, 4, 10, 29, 97, 366, 1534, 7050, 35167, 188835, 1084180, 6618472, 42756208, 291120551, 2081922515, 15590248868, 121920095674, 993343650912, 8414029179365, 73953763887277, 673316834487162, 6340176007793060, 61657373569634586, 618445940056365121 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..400

EXAMPLE

For n=3 the a(3) = 10 partitions are {}, 1, 2, 3, 1|2, 13, 1|3, 2|3, 13|2, 1|2|3.

MAPLE

g:= proc(n, l, t) option remember; `if`(n=0, 1, add(`if`(l>0

      and j=l, 0, g(n-1, j, `if`(j=t, t+1, t))), j=0..t))

    end:

a:= n-> g(n, 0, 1):

seq(a(n), n=0..30);

MATHEMATICA

g[n_, l_, t_] := g[n, l, t] = If[n==0, 1, Sum[If[l>0 && j==l, 0, g[n-1, j, If[j==t, t+1, t]]], {j, 0, t}]]; a[n_] := g[n, 0, 1]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Feb 04 2017, translated from Maple *)

CROSSREFS

Cf. A247100, A261134, A261489, A261492.

Sequence in context: A086631 A230957 A279552 * A047051 A271077 A126349

Adjacent sequences:  A261038 A261039 A261040 * A261042 A261043 A261044

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 09 2015

STATUS

approved

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Last modified October 18 07:00 EDT 2018. Contains 316307 sequences. (Running on oeis4.)