login
A060696
Number of permutations in S_n avoiding the strings 123, 321 and 231.
4
1, 1, 2, 3, 5, 11, 23, 63, 153, 489, 1329, 4785, 14235, 56475, 181215, 780255, 2672145, 12348945, 44781345, 220253985, 840523635, 4370620275, 17465201775, 95498916975, 397983749625, 2278224696825, 9867844134225, 58917607974225
OFFSET
0,3
LINKS
S. Kitaev, Multi-avoidance of generalized patterns, Discrete Math., 260 (2003), 89-100.
FORMULA
a(0)=1, a(1)=1, a(2)=2, a(3)=3, a(n) = (n-2)a(n-2)+(n-3)!! for n >= 4
E.g.f. for A(n)=a(n+1) (n>=0): (1+x)*exp(x^2/2)*(1+sqrt(Pi/2)*erf(x/sqrt(2))), where erf denotes the error function. - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 01 2002
a(n) = (n-1)!!+(n-2)!! (cf. A006882).
EXAMPLE
a(5) = (5-1)!! + (5-2)!! = 4!! + 3!! = 2*4 + 1*3 = 11.
MATHEMATICA
Join[{1, 1}, Table[(n - 1)!! + (n - 2)!! , {n, 2, 50}]] (* G. C. Greubel, May 23 2017 *)
CROSSREFS
Cf. A011782.
Sequence in context: A261810 A176499 A175234 * A076051 A000628 A358554
KEYWORD
nonn
AUTHOR
Tuwani A. Tshifhumulo (tat(AT)univen.ac.za), Apr 20 2001
EXTENSIONS
Corrected and extended by Vladeta Jovovic, Apr 22 2001
STATUS
approved