A116834 Number of permutations of length n which avoid the patterns 1234, 2431, 3421.

1, 2, 6, 21, 73, 222, 563, 1226, 2376, 4213, 6972, 10923, 16371, 23656, 33153, 45272, 60458, 79191, 101986, 129393, 161997, 200418, 245311, 297366, 357308, 425897, 503928, 592231, 691671, 803148, 927597, 1065988, 1219326, 1388651, 1575038, 1779597, 2003473

Offset

1,2

Links

Table of n, a(n) for n=1..37.

David Callan and Toufik Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 [math.CO], 2017, Table 2 No 60.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: -x*(x^6+16*x^5+13*x^4+x^3+6*x^2-3*x+1)/(x-1)^5.

For n >= 3, a(n) = (35*n^4 - 390*n^3 + 1729*n^2 - 3438*n + 2592)/24. - Franklin T. Adams-Watters, Sep 16 2006

Crossrefs

Sequence in context: A360153 A294759 A294760 * A116762 A116803 A116829

Adjacent sequences: A116831 A116832 A116833 * A116835 A116836 A116837

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Extensions

More terms from Jason Yuen, Sep 18 2025

Status

approved