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A261134 Number of partitions of subsets s of {1,...,n}, where all integers belonging to a run of consecutive members of s are required to be in different parts. 5
1, 2, 4, 9, 23, 66, 209, 722, 2697, 10825, 46429, 211799, 1023304, 5217048, 27974458, 157310519, 925326848, 5680341820, 36315837763, 241348819913, 1664484383610, 11893800649953, 87931422125632, 671699288516773, 5295185052962371, 43029828113547685 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..32

EXAMPLE

a(3) = 9: {}, 1, 2, 3, 1|2, 2|3, 13, 1|3, 1|2|3.

a(4) = 23: {}, 1, 2, 3, 4, 1|2, 1|3, 13, 1|4, 14, 2|3, 2|4, 24, 3|4, 1|2|3, 1|2|4, 1|24, 14|2, 1|3|4, 13|4, 14|3, 2|3|4, 1|2|3|4.

MAPLE

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

      `if`(j in s, 0, g(n-1, `if`(j=0, {}, s union {j}),

      `if`(j=t, t+1, t))), j=0..t))

    end:

a:= n-> g(n, {}, 1):

seq(a(n), n=0..20);

MATHEMATICA

g[n_, s_List, t_] := g[n, s, t] = If[n == 0, 1, Sum[If[MemberQ[s, j], 0, g[n-1, If[j == 0, {}, s ~Union~ {j}], If[j == t, t+1, t]]], {j, 0, t}]]; a[n_] := g[n, {}, 1]; Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Feb 04 2017, translated from Maple *)

CROSSREFS

Cf. A247100, A261041, A261489, A261492.

Sequence in context: A202552 A272301 A129698 * A117419 A124461 A026898

Adjacent sequences:  A261131 A261132 A261133 * A261135 A261136 A261137

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 10 2015

STATUS

approved

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Last modified October 22 04:29 EDT 2018. Contains 316431 sequences. (Running on oeis4.)