|
|
A328437
|
|
Number of inversion sequences of length n avoiding the consecutive pattern 001.
|
|
16
|
|
|
1, 1, 2, 4, 11, 42, 210, 1292, 9352, 77505, 722294, 7470003, 84854788, 1049924370, 14052654158, 202271440732, 3115338658280, 51118336314648, 890201500701303, 16397264064993185, 318505677099378561, 6506565509515408206, 139449260758011488550, 3128599281190613701180
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
A length n inversion sequence e_1e_2...e_n is a sequence of integers such that 0 <= e_i < i. The term a(n) counts the inversion sequences of length n with no entries e_i, e_{i+1}, e_{i+2} such that e_i = e_{i+1} < e_{i+2}. That is, a(n) counts the inversion sequences of length n avoiding the consecutive pattern 001.
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ n! * c / sqrt(n), where c = 0.549342310436989831962783548104445992522... - Vaclav Kotesovec, Oct 18 2019
|
|
EXAMPLE
|
The a(4)=11 length 4 inversion sequences avoiding the consecutive pattern 001 are 0000, 0100, 0110, 0120, 0101, 0111, 0121, 0102, 0122, 0103, and 0123.
|
|
MAPLE
|
b := proc(n, x, t) option remember; `if`(n = 0, 1, add(
`if`(t and i = x, 0, b(n - 1, i, i < x)), i = 0 .. n - 1))
end proc:
a := n -> b(n, -1, false):
seq(a(n), n = 0 .. 24);
|
|
MATHEMATICA
|
b[n_, x_, t_] := b[n, x, t] = If[n == 0, 1, Sum[If[t && i == x, 0, b[n - 1, i, i < x]], {i, 0, n - 1}]];
a[n_] := b[n, -1, False];
|
|
CROSSREFS
|
Cf. A328357, A328358, A328429, A328430, A328431, A328432, A328433, A328434, A328435, A328436, A328438, A328439, A328440, A328441, A328442.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|