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A116768
Number of permutations of length n which avoid the patterns 1342, 3214, 4213.
1
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
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.
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
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
STATUS
approved