A319536 Number of signed permutations of length n where numbers occur in consecutive order.
0, 2, 14, 122, 1278, 15802, 225886, 3670074, 66843902, 1349399162, 29912161758, 722399486074, 18881553923326, 531063524702778, 15993786127174238, 513533806880120762, 17512128958240460286, 632099987274779910394, 24076353238897830158302
Offset: 1
Keywords
Examples
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.
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
Programs
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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}] -
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)) # usage: checkFunc({desired permutation length})
Comments