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A328507
Number of inversion sequences of length n avoiding the consecutive pattern 101.
1
1, 1, 2, 6, 23, 109, 619, 4113, 31352, 269841, 2589026, 27404677, 317265161, 3988181568, 54099618419, 787705115000, 12253696410675, 202831037178017, 3559585021719875, 66018657264425355, 1290284788431977106, 26505045303122642171, 570918508059059670322
OFFSET
0,3
LINKS
Juan S. Auli, Pattern Avoidance in Inversion Sequences, Ph. D. thesis, Dartmouth College, ProQuest Dissertations Publishing (2020), 27964164.
Juan S. Auli, Sergi Elizalde, Consecutive Patterns in Inversion Sequences, arXiv:1904.02694 [math.CO], 2019. See Table 4.
FORMULA
a(n) ~ n! * c / sqrt(n), where c = 2.48988835987151440021135203237... - Vaclav Kotesovec, Oct 19 2019
MAPLE
b:= proc(n, j, t) option remember; `if`(n=0, 1, add(
`if`(i<=j or i<>t, b(n-1, i, j), 0), i=1..n))
end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..25); # Alois P. Heinz, Oct 18 2019
MATHEMATICA
b[n_, j_, t_] := b[n, j, t] = If[n == 0, 1, Sum[If[i <= j || i != t, b[n-1, i, j], 0], {i, 1, n}]];
a[n_] := b[n, 0, 0];
a /@ Range[0, 25] (* Jean-François Alcover, Mar 19 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved