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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]==(2n-1)*a[n-1]+2(n-2)*a[n-2], 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(n-1):

            a = perm_literal[i]

            if perm_literal[i + 1] == a + 1:

                permset.remove(perm)

                break

    print((factorial(n)*(2^n))-len(permset))

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

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Last modified May 20 20:16 EDT 2019. Contains 323426 sequences. (Running on oeis4.)