A207821 Number of permutations of [n] that either have a fixed point or a succession, but not both.

0, 1, 0, 5, 12, 69, 370, 2609, 20552, 183249, 1817794, 19867793, 237126320, 3068483277, 42788761294, 639619513669, 10202914060472, 172984071549421, 3106257794721534, 58892020126278457, 1175554242034515780

Offset

0,4

Comments

A succession of a permutation p is the appearance of [k,k+1], e.g. in 23541, 23 is a succession.

Links

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

Example

a(4) = 12 because we have 1324, 1432, 2341, 2431, 3214, 3241, 3412, 3421, 4123, 4132, 4213 and 4312.

Prog

(PARI) A207821(n)=my(p, c); sum(k=1, n!, p=numtoperm(n, k); c=(p[1]==1); for(j=2, n, p[j]==j & c<=0 & !c++ & break; p[j]-1==p[j-1] & c>=0 & !c-- & break); c!=0) \\ - M. F. Hasler, Jan 13 2013

Crossrefs

Cf. A000166, A002467, A180191, A201452, A207819.

Sequence in context: A246176 A009413 A009429 * A297644 A242043 A156236

Adjacent sequences: A207818 A207819 A207820 * A207822 A207823 A207824

Keyword

nonn,more

Author

Jon Perry, Jan 10 2013

Extensions

Values a(1) to a(10) double-checked by M. F. Hasler, Jan 13 2013

Inserted a(0) and a(11)-a(13) from Alois P. Heinz, Jan 18 2013

a(14)-a(20) from Alois P. Heinz, Jul 05 2021

Status

approved