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
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