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A328434
Number of inversion sequences of length n avoiding the consecutive patterns 101, 102, 201, and 210.
15
1, 1, 2, 6, 21, 81, 346, 1630, 8350, 45958, 269815, 1681285, 11071336, 76743040, 558062437, 4244853573, 33687390663, 278296576327, 2388351295760, 21254019548162, 195801111412320, 1864508416302520, 18326903140310011, 185711672802101781, 1937795878138303715
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, 201, and 210.
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, 201, and 210 are 0101, 0102 and 0103.
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 and x>-1)), 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 && x > -1]], {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 16 2019
STATUS
approved