A116838 Number of permutations of length n which avoid the patterns 1342, 3421, 4312.

1, 2, 6, 21, 72, 233, 719, 2146, 6260, 17968, 50967, 143278, 399960, 1110203, 3067479, 8442903, 23163006, 63371999, 172967309, 471115792, 1280844662, 3476636122, 9423007521, 25506378316, 68958653982, 186231636833

Offset

1,2

Links

Table of n, a(n) for n=1..26.

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 53.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (13,-72,222,-418,496,-369,165,-40,4).

Formula

G.f.: x*(x^9 -8x^8 +34x^7 -97x^6 +183x^5 -205x^4 +135x^3 -52x^2 +11x -1)/((x^2-3x+1)^2 (2x-1)^2 (x-1)^3).

Mathematica

CoefficientList[Series[(x^9 - 8 x^8 + 34 x^7 - 97 x^6 + 183 x^5 - 205 x^4 + 135 x^3 - 52 x^2 + 11 x - 1)/((x^2 - 3 x + 1)^2 (2 x - 1)^2 (x - 1)^3), {x, 0, 30}], x] (* Wesley Ivan Hurt, Dec 28 2023 *)

Crossrefs

Sequence in context: A294703 A116800 A116758 * A116836 A116796 A116779

Adjacent sequences: A116835 A116836 A116837 * A116839 A116840 A116841

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved