|
|
A258690
|
|
Total number of longest increasing runs in all permutations of [n].
|
|
1
|
|
|
1, 1, 3, 8, 32, 167, 1096, 8117, 67859, 627649, 6394781, 71201812, 861677250, 11270215084, 158564826122, 2389093936957, 38396351412220, 655832914215010, 11865953978478454, 226724258401651143, 4562163514498852598, 96430112680094188086, 2136024671422363671272
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
a(0) = 1 by convention.
|
|
LINKS
|
|
|
EXAMPLE
|
a(1) = 1: (1).
a(2) = 3: (12), (2)(1).
a(3) = 8: (123), (13)2, 2(13), (23)1, 3(12), (3)(2)(1).
|
|
MAPLE
|
b:= proc(u, o, l, m, c) option remember; `if`(u+o=0, `if`(l>m, 1,
`if`(l<m, c, c+1)), add(b(u-j, o+j-1, 1, max(l, m),
`if`(l>m, 1, `if`(l<m, c, c+1))), j=1..u)+
add(b(u+j-1, o-j, l+1, m, c), j=1..o))
end:
a:= n-> b(n, 0$4):
seq(a(n), n=0..25);
|
|
MATHEMATICA
|
b[u_, o_, l_, m_, c_] := b[u, o, l, m, c] = If[u + o == 0, If[l > m, 1,
If[l < m, c, c + 1]], Sum[b[u - j, o + j - 1, 1, Max[l, m],
If[l > m, 1, If[l < m, c, c + 1]]], {j, 1, u}] +
Sum[b[u+j-1, o-j, l+1, m, c], {j, 1, o}]];
a[n_] := b[n, 0, 0, 0, 0];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|