|
|
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
|
|
|
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-François Alcover, Feb 04 2017, translated from Maple *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|