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A084894
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Number of permutations of length n such that at least one absolute difference between consecutive elements has a distinct partner.
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2
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0, 0, 2, 20, 112, 696, 5008, 40280, 362760, 3628504, 39916152, 479000272, 6227017600, 87178281288, 1307674342408, 20922789832080, 355687427952808, 6402373705217304, 121645100407380704, 2432902008173142656, 51090942171698988176, 1124000727777569109296
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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a(3)=2 as only 123 and 321 have the required property, with differences of 1,1. The rest all have differences of 1,2.
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MATHEMATICA
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A006967 = Cases[Import["https://oeis.org/A006967/b006967.txt", "Table"], {_, _}][[All, 2]];
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PROG
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(PARI) { for (n=3, 10, x=vector(n-1); s=0; for (i=1, n!, v=numtoperm(n, i); for (j=1, n-1, x[j]=abs(v[j+1]-v[j])); x=vecsort(x); fl=0; for (k=1, n-2, if (x[k]==x[k+1], fl=1; break)); if (fl==1, s++)); print(n"; "s)) }
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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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