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Search: id:A084894
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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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+0
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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n)=n!-A006967(n)
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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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PROGRAM
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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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Cf. A006967.
Sequence in context: A073077 A069537 A001797 this_sequence A061004 A062189 A094254
Adjacent sequences: A084891 A084892 A084893 this_sequence A084895 A084896 A084897
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Jun 10 2003
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