OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..250
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 3.
FORMULA
a(n) ~ n! * c * d^n * n^alfa, where d = 1/A240885 = 1/(sqrt(2) * InverseErf(sqrt(2/Pi))), alfa = 0.294868853646259565..., c = 2.22826071050847602... - 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 01 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec and Juan S. Auli, Oct 17 2019
STATUS
approved