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A095816 Number of permutations of 1..n with no three elements in correct or reverse order. 9
1, 1, 2, 4, 18, 92, 570, 4082, 33292, 304490, 3086890, 34357812, 416526730, 5463479106, 77094352076, 1164544912938, 18749754351338, 320544941916628, 5799226664694602, 110695180631374114, 2223242026407894732 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Counts permutations with the property that no subsequence i(i+1)(i+2) or (i+2)(i+1)i occurs.

LINKS

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.

FORMULA

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

PROG

(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

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Jonas Wallgren, Jun 08 2004

EXTENSIONS

More terms from Ivana Jovovic ( ivana121(AT)EUnet.yu ), Nov 11 2007

a(0)=1 prepended by Max Alekseyev, Jun 14 2011

STATUS

approved

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Last modified July 8 05:33 EDT 2020. Contains 335513 sequences. (Running on oeis4.)