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A095816
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Number of permutations of 1..n with no three elements in correct or reverse order.
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10
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1, 1, 2, 4, 18, 92, 570, 4082, 33292, 304490, 3086890, 34357812, 416526730, 5463479106, 77094352076, 1164544912938, 18749754351338, 320544941916628, 5799226664694602, 110695180631374114, 2223242026407894732
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OFFSET
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0,3
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COMMENTS
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Counts permutations with the property that no subsequence i(i+1)(i+2) or (i+2)(i+1)i occurs.
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 0..200
W. M. Dymacek, I. Lambert, Permutations Avoiding Runs of i, i+1, i+2 or i, i-1, i-2 , J. Int. Seq. 14 (2011) # 11.1.6, Table 1.
D. M. Jackson and R. C. Read, A note on permutations without runs of given length, Aequationes Math. 17 (1978), no. 2-3, 336-343.
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FORMULA
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G.f. Sum_{n>=0} n!*((2*x^m-x^(m+1)-x)/(x^m-1))^n where m = 3. - Ivana Jovovic ( ivana121(AT)EUnet.yu ), Nov 11 2007
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PROG
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(PARI) seq(n)={my(m=3); Vec(sum(k=0, n, k!*((2*x^m-x^(m+1)-x)/(x^m-1) + O(x*x^n))^k))} \\ Andrew Howroyd, Aug 31 2018
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CROSSREFS
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Cf. A002464, A095817, A095818.
Cf. A165963, A165964, A078628. [From Isaac Lambert, Oct 07 2009]
Sequence in context: A295370 A292280 A120664 * A020101 A099938 A135069
Adjacent sequences: A095813 A095814 A095815 * A095817 A095818 A095819
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KEYWORD
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nonn
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AUTHOR
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Jonas Wallgren, Jun 08 2004
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EXTENSIONS
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More terms from Ivana Jovovic ( ivana121(AT)EUnet.yu ), Nov 11 2007
a(0)=1 prepended by Max Alekseyev, Jun 14 2011
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STATUS
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approved
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