

A319536


Number of signed permutations of length n where numbers occur in consecutive order.


1



0, 2, 14, 122, 1278, 15802, 225886, 3670074, 66843902, 1349399162, 29912161758, 722399486074, 18881553923326, 531063524702778, 15993786127174238, 513533806880120762, 17512128958240460286, 632099987274779910394, 24076353238897830158302
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

a(n) also represents the number of reducible signed permutations of length n. A permutation is reducible when an adjacency occurs in the permutation.
The first 8 terms of this sequence were found by exhaustive search of all signed permutations.


REFERENCES

Manaswinee Bezbaruah, Henry Fessler, Leigh Foster, Marion Scheepers, George Spahn, Context Directed Sorting: Robustness and Complexity, draft.


LINKS

Leigh Foster, Table of n, a(n) for n = 1..50


FORMULA

a(n) = A000165(n)  A271212(n).


EXAMPLE

Of the 8 signed permutations of length 2: {[1,2], [1,2], [1,2], [1,2], [2,1], [2,1], [2,1], [2,1]} only two are reducible: [1,2] and [2,1]. Thus a(2) = 2.


MATHEMATICA

Table[(2 n)!!, {n, 1, 20}]  RecurrenceTable[{a[n]==(2n1)*a[n1]+2(n2)*a[n2], a[0]==1, a[1]==2}, a[n], {n, 1, 20}]


PROG

(SageMath)
from ast import literal_eval
def checkFunc(n):
p = SignedPermutations(n)
permlist = p.list()
permset = set(permlist)
for perm in permlist:
perm_literal = literal_eval(str(perm))
for i in range(n1):
a = perm_literal[i]
if perm_literal[i + 1] == a + 1:
permset.remove(perm)
break
print(factorial(n)*(2^n)len(permset))
# usage: checkFunc({desired permutation length})


CROSSREFS

Cf. A000165, A271212.
Sequence in context: A267906 A199560 A283184 * A060468 A121082 A216595
Adjacent sequences: A319533 A319534 A319535 * A319537 A319538 A319539


KEYWORD

nonn


AUTHOR

Leigh Foster, Sep 22 2018


STATUS

approved



