A285672 Number of permutations p of [n] avoiding consecutive odd sums i+p(i), (i+1)+p(i+1) for all i in [n-1].

1, 1, 1, 2, 8, 36, 180, 1008, 6336, 46080, 374400, 3369600, 32659200, 344736000, 3886444800, 47348582400, 611264102400, 8442272563200, 122595843686400, 1890952003584000, 30510694932480000, 520011800985600000, 9231875243458560000, 172292221923655680000

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..466

Example

a(0) = 1: the empty permutation.
a(1) = 1: 1.
a(2) = 1: 12.
a(3) = 2: 123, 321.
a(4) = 8: 1234, 1432, 2413, 2431, 3214, 3412, 4213, 4231.
a(5) = 36: 12345, 12543, 13524, 13542, 14325, 14523, 15324, 15342, 24135, 24153, 24315, 24351, 24513, 24531, 31524, 31542, 32145, 32541, 34125, 34521, 35124, 35142, 42135, 42153, 42315, 42351, 42513, 42531, 51324, 51342, 52143, 52341, 53124, 53142, 54123, 54321.

Maple

b:= proc(n, i, j, p, t) option remember; `if`(n=0, 1,
     `if`(i=0 or t=1 and p=1, 0, i*b(n-1, i-1, j, 1-p, p))+
     `if`(j=0 or t=1 and p=0, 0, j*b(n-1, i, j-1, 1-p, 1-p)))
    end:
a:= n-> b(n, floor(n/2), ceil(n/2), 1, 0):
seq(a(n), n=0..25);

Mathematica

b[n_, i_, j_, p_, t_] := b[n, i, j, p, t] =
     If[n==0, 1, If[i==0 || t ==1 && p==1, 0, i*b[n-1, i-1, j, 1-p, p]] +
     If[j==0 || t==1 && p==0, 0, j*b[n-1, i, j-1, 1-p, 1-p]]];
a[n_] := b[n, Floor[n/2], Ceiling[n/2], 1, 0];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Aug 30 2021, after Alois P. Heinz *)

Crossrefs

Cf. A199660, A231601.

Sequence in context: A227791 A245102 A129148 * A081958 A369619 A316663

Adjacent sequences: A285669 A285670 A285671 * A285673 A285674 A285675

Keyword

nonn

Author

Alois P. Heinz, Apr 24 2017

Status

approved