|
| |
|
|
A230130
|
|
Number of permutations of order n with the length of longest run equal 7.
|
|
3
|
|
|
|
2, 28, 362, 4720, 64020, 913440, 13760472, 219040274, 3681354658, 65231186514, 1216489698082, 23832126613268, 489566931234322, 10526180908026522, 236475437787567496, 5541690642862917134, 135258139216049657102, 3433304061341792767884, 90508485528963754208076
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
7,1
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 7..450
|
|
|
MAPLE
|
g:= proc(u, o, t) option remember; `if`(u+o=0, 1,
add(g(o+j-1, u-j, 2), j=1..u) +`if`(t<7,
add(g(u+j-1, o-j, t+1), j=1..o), 0))
end:
b:= proc(u, o, t) option remember; `if`(t=7, g(u, o, t),
add(b(o+j-1, u-j, 2), j=1..u)+
add(b(u+j-1, o-j, t+1), j=1..o))
end:
a:= n-> add(b(j-1, n-j, 1), j=1..n):
seq(a(n), n=7..30);
|
|
|
MATHEMATICA
|
length = 7;
g[u_, o_, t_] := g[u, o, t] = If[u+o == 0, 1, Sum[g[o + j - 1, u - j, 2], {j, 1, u}] + If[t<length, Sum[g[u + j - 1, o - j, t+1], {j, 1, o}], 0]];
b[u_, o_, t_] := b[u, o, t] = If[t == length, g[u, o, t], Sum[b[o + j - 1, u - j, 2], {j, 1, u}] + Sum[b[u + j - 1, o - j, t + 1], {j, 1, o}]];
a[n_] := Sum[b[j - 1, n - j, 1], {j, 1, n}];
Table[a[n], {n, length, 30}] (* Jean-François Alcover, Aug 18 2018, after Alois P. Heinz *)
|
|
|
CROSSREFS
|
Column l=7 of A211318.
A diagonal of A010026.
Sequence in context: A281320 A152280 A061629 * A011944 A271565 A241365
Adjacent sequences: A230127 A230128 A230129 * A230131 A230132 A230133
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Alois P. Heinz, Oct 10 2013
|
|
|
STATUS
|
approved
|
| |
|
|
