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A370767
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Number of signed permutations of length n+1 with adjacent elements differing by more than 1 and whose first element is 1.
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4
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1, 1, 3, 17, 139, 1401, 16867, 236513, 3787707, 68219081, 1364931859, 30037136433, 721044433387, 18750182814233, 525071095004739, 15753703863875201, 504159100060894747, 17142539126080474473, 617165134818228049267, 23453349764127439545041
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OFFSET
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0,3
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COMMENTS
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A signed permutation is a sequence (x_1,x_2,...,x_n) of integers such that {|x_1|,|x_2|,...|x_n|} = {1,2...,n}.
Adjacent elements that differ in sign will always differ by more than 1.
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LINKS
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FORMULA
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A283184(n) = a(n) - a(n-1) for n > 0.
a(n) = (1+2*n)*a(n-1) + (3-2*n)*a(n-2) + (5-2*n)*a(n-3) + (-4+2*n)*a(n-4) for n >= 4.
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EXAMPLE
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In the following examples, the number of assignments of signs to each unsigned permutation is shown in parenthesis.
a(2) = 3: 123(1), 132(2). Total is 1 + 2 = 3.
a(3) = 17: 1234(1), 1243(2), 1324(4), 1342(4), 1423(4), 1432(2).
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PROG
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(PARI) a(n)=subst(serlaplace(polcoef(1/(1 + (1 - 2*y)*x + 2*y*x^2) + O(x*x^n), n)), y, 1)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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