A116832 Number of permutations of length n which avoid the patterns 1324, 3421, 4123.

1, 2, 6, 21, 70, 203, 517, 1187, 2504, 4921, 9107, 16009, 26922, 43567, 68177, 103591, 153356, 221837, 314335, 437213, 598030, 805683, 1070557, 1404683, 1821904, 2338049, 2971115, 3741457, 4671986, 5788375, 7119273, 8696527, 10555412, 12734869, 15277751

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 12.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: x*(1 - 5*x + 13*x^2 - 14*x^3 + 14*x^4 - 7*x^5 + 6*x^6 + 3*x^7 - 4*x^8 + x^9) / (1 - x)^7.

For n >= 4, a(n) = (2*n^6 - 21*n^5 + 125*n^4 - 255*n^3 - 217*n^2 + 1266*n - 180)/180. - Franklin T. Adams-Watters, Sep 16 2006

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>10. - Colin Barker, Oct 23 2017

Prog

(PARI) Vec(x*(1 - 5*x + 13*x^2 - 14*x^3 + 14*x^4 - 7*x^5 + 6*x^6 + 3*x^7 - 4*x^8 + x^9) / (1 - x)^7 + O(x^50)) \\ Colin Barker, Oct 23 2017

Crossrefs

Sequence in context: A116765 A116815 A116804 * A116811 A294718 A116794

Adjacent sequences: A116829 A116830 A116831 * A116833 A116834 A116835

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved