A116768 Number of permutations of length n which avoid the patterns 1342, 3214, 4213.

1, 2, 6, 21, 73, 239, 738, 2178, 6220, 17351, 47595, 128985, 346492, 924788, 2456502, 6502017, 17164189, 45219875, 118954134, 312559974, 820560736, 2152792187, 5645155791, 14797355181, 38776269808, 101590174424, 266111693898, 696979788213, 1825297432705

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 [math.CO] (2017), Table 2 No 85.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (7,-18,21,-11,2).

Formula

G.f.: x*(1 - 5*x + 10*x^2 - 6*x^3 + 3*x^4) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x + x^2)).

a(n) = 2^(-1-n)*(-7*4^n+5*(3+sqrt(5))^n - sqrt(5)*(3+sqrt(5))^n + (3-sqrt(5))^n*(5+sqrt(5)) + 3*2^(1+n)*n). - Colin Barker, Nov 02 2017

a(n) = 3*n + 5*Fibonacci(2*n - 1) - 7*2^(n - 1). - Ehren Metcalfe, Nov 08 2017

Mathematica

LinearRecurrence[{7, -18, 21, -11, 2}, {1, 2, 6, 21, 73}, 40] (* Harvey P. Dale, Jan 16 2019 *)

Prog

(PARI) Vec(x*(1 - 5*x + 10*x^2 - 6*x^3 + 3*x^4) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x + x^2)) + O(x^30)) \\ Colin Barker, Nov 02 2017

Crossrefs

Sequence in context: A116776 A116754 A294801 * A294694 A116740 A294802

Adjacent sequences: A116765 A116766 A116767 * A116769 A116770 A116771

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved