A116828 Number of permutations of length n which avoid the patterns 2413, 3421, 4123.

1, 2, 6, 21, 73, 245, 804, 2617, 8511, 27709, 90283, 294231, 958826, 3124175, 10178664, 33160777, 108030912, 351937426, 1146512182, 3734982701, 12167348792, 39637060036, 129123584284, 420638265356, 1370286347625

Offset

1,2

Links

Table of n, a(n) for n=1..25.

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 [math.CO] (2017), Table 2 No 110.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (10,-42,100,-150,144,-86,27,-2,-1).

Formula

G.f.: (-x*(x^8+2x^7-18x^6+47x^5-65x^4+55x^3-28x^2+8x-1)) / (1+x^9+2x^8-27x^7+86x^6-144x^5+150x^4-100x^3+42x^2-10x). [Corrected by Georg Fischer, May 19 2019]

Mathematica

CoefficientList[Series[(-x*(x^8+2x^7-18x^6+47x^5-65x^4+55x^3-28x^2+8x-1)) / (1+x^9+2x^8-27x^7+86x^6-144x^5+150x^4-100x^3+42x^2-10x), {x, 0, 25}], x] (* Georg Fischer, May 19 2019 *)

Crossrefs

Sequence in context: A294697 A116826 A116760 * A294764 A116837 A116781

Adjacent sequences: A116825 A116826 A116827 * A116829 A116830 A116831

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved