

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
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OFFSET

0,2


LINKS



EXAMPLE

a(3) = 9: {}, 1, 2, 3, 12, 23, 13, 13, 123.
a(4) = 23: {}, 1, 2, 3, 4, 12, 13, 13, 14, 14, 23, 24, 24, 34, 123, 124, 124, 142, 134, 134, 143, 234, 1234.


MAPLE

g:= proc(n, s, t) option remember; `if`(n=0, 1, add(
`if`(j in s, 0, g(n1, `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[n1, 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}] (* JeanFrançois Alcover, Feb 04 2017, translated from Maple *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



