login
A328435
Number of inversion sequences of length n avoiding the consecutive patterns 101, 102, and 201.
15
1, 1, 2, 6, 21, 83, 368, 1814, 9837, 58095, 370499, 2534374, 18493023, 143280489, 1173971656, 10136279104, 91936857611, 873547634921, 8673546319685, 89796095349193, 967384904147690, 10825116242427973, 125613702370667158, 1509222589338456874, 18748890945849736182
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}. This is the same as the set of inversion sequences of length n avoiding the consecutive patterns 101, 102, and 201.
LINKS
EXAMPLE
Note that a(4)=21. Indeed, of the 24 inversion sequences of length 4, the only ones that do not avoid the consecutive patterns 101, 102, and 201 are 0101, 0102, and 0103.
MAPLE
b := proc(n, x, t) option remember; `if`(n = 0, 1, add(
`if`(t and x < i, 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 && x < i, 0, b[n - 1, i, i < x]], {i, 0, n - 1}]];
a[n_] := b[n, -1, False];
a /@ Range[0, 24] (* Jean-François Alcover, Mar 02 2020 after Alois P. Heinz in A328357 *)
KEYWORD
nonn
AUTHOR
Juan S. Auli, Oct 17 2019
STATUS
approved