A095816 Number of permutations of 1..n with no three elements in correct or reverse order.

1, 1, 2, 4, 18, 92, 570, 4082, 33292, 304490, 3086890, 34357812, 416526730, 5463479106, 77094352076, 1164544912938, 18749754351338, 320544941916628, 5799226664694602, 110695180631374114, 2223242026407894732, 46868311165318977130, 1034758905785710599402

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 and 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

From Vaclav Kotesovec, May 26 2023: (Start)

a(n) ~ n! * (1 - 2/n + 6/n^2 - 28/(3*n^3) - 10/(3*n^4) + 496/(15*n^5) + 1384/(45*n^6) - 79724/(315*n^7) - 259306/(315*n^8) + 3718094/(2835*n^9) + 33233992/(2025*n^10) + ...).

a(n) = (n-3)*a(n-1) + 3*(n-1)*a(n-2) + (2*n-5)*a(n-3) - (n-3)*a(n-4) - (2*n-13)*a(n-5) - (n-8)*a(n-6) + (n-6)*a(n-7).

(End)

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 A370524 A099938

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