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A209322 Number of derangements of [n] with no succession. 3
1, 0, 1, 0, 4, 14, 102, 682, 5484, 49288, 492812, 5418154, 64993966, 844658714, 11822116868, 177292309424, 2836140479376, 48206588630826, 867597809813018, 16482372327022854, 329612875955466784 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A derangement is a permutation with no fixed points. A succession of a permutation p is a position i such that p(i+1)-p(i) = 1.

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(n) = n! - A207819(n).

EXAMPLE

For n=4 we have 2143, 2413, 3142 and 4321, so a(4) = 4.

MAPLE

F:= proc(S) add(G(S minus {s}, s-1), s = S minus {nops(S)}) end proc:

G:= proc(S, t) option remember;

if S = {} then return 1 fi;

add(procname(S minus {s}, s-1), s = S minus {t, nops(S)})

end proc:

1, seq(F({$1..n}), n=1..19); # Robert Israel, Mar 02 2017

MATHEMATICA

F[{}] = 1; F[S_] := Sum[G[S ~Complement~ {s}, s-1], {s, S ~Complement~ {Length[S]}}];

G[{}, _] = 1; G[S_, t_] := G[S, t] = Sum[G[S ~Complement~ {s}, s-1], {s, S ~Complement~ {t, Length[S]}}];

Table[a[n] = F[Range[n]]; Print[n, " ", a[n]]; a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Mar 05 2019, after Robert Israel *)

CROSSREFS

Cf. A000166, A002467, A180191, A207819, A207821, A209325, A209326.

Sequence in context: A316414 A268689 A299199 * A110302 A282617 A005743

Adjacent sequences:  A209319 A209320 A209321 * A209323 A209324 A209325

KEYWORD

nonn,more

AUTHOR

Jon Perry, Jan 19 2013

EXTENSIONS

a(11)-a(14) from Alois P. Heinz, Jan 19 2013

a(15)-a(20) from Robert Israel, Mar 02 2017

STATUS

approved

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Last modified May 17 19:26 EDT 2021. Contains 343988 sequences. (Running on oeis4.)