OFFSET
0,3
LINKS
D. I. Bevan, On the growth of permutation classes, PhD thesis, The Open University, 2015.
Robert Brignall, Jakub Sliacan, Combinatorial specifications for juxtapositions of permutation classes, arXiv:1902.02705 [math.CO], 2019.
Index entries for linear recurrences with constant coefficients, signature (10,-40,82,-91,52,-12).
FORMULA
G.f: 1/(1-z) + z^2/((1-z)^2*(1-2*z)) + z^3*(1+z-4*z^2)/((1-z)^3*(1-2*z)^2*(1-3*z)).
a(n) = Sum_{k=0..3} A123125(n,k). - Alois P. Heinz, Sep 11 2019
a(n) = 3^n -n*2^n +n^2/2 -n/2. - R. J. Mathar, Sep 25 2019
EXAMPLE
For n=4, a(4) = 23 because the permutation 4321 is the only one of length 4 to have more than 2 descents.
MAPLE
b:= proc(u, o, k) option remember;
`if`(u+o=0, 1, add(b(u-j, o+j-1, k), j=1..u)+
`if`(k<2, add(b(u+j-1, o-j, k+1), j=1..o), 0))
end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..28); # Alois P. Heinz, Sep 11 2019
MATHEMATICA
LinearRecurrence[{10, -40, 82, -91, 52, -12}, {1, 1, 2, 6, 23, 93}, 30] (* Jean-François Alcover, Mar 01 2020 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Brignall, Sep 11 2019
STATUS
approved