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A116707
Number of permutations of length n which avoid the patterns 1342, 4213.
1
1, 2, 6, 22, 86, 338, 1318, 5106, 19718, 76066, 293398, 1131794, 4366374, 16846018, 64995254, 250765298, 967503814, 3732821922, 14401956182, 55565542354, 214382633062, 827129764994, 3191227078902, 12312373271986, 47503525349126, 183277819294562
OFFSET
1,2
LINKS
Darla Kremer and Wai Chee Shiu, Finite transition matrices for permutations avoiding pairs of length four patterns, Discrete Math. 268 (2003), 171-183. MR1983276 (2004b:05006). See Table 1.
FORMULA
G.f.: -x*(x-1)*(2*x-1)^2 / (4*x^4-16*x^3+16*x^2-7*x+1).
a(n) = 7*a(n-1) - 16*a(n-2) + 16*a(n-3) - 4*a(n-4) for n>3. - Colin Barker, Oct 20 2017
MATHEMATICA
CoefficientList[Series[-(x - 1)*(2*x - 1)^2/(4*x^4 - 16*x^3 + 16*x^2 - 7*x + 1), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 04 2022 *)
PROG
(PARI) Vec(x*(1 - x)*(1 - 2*x)^2 / (1 - 7*x + 16*x^2 - 16*x^3 + 4*x^4) + O(x^40)) \\ Colin Barker, Oct 20 2017
CROSSREFS
Sequence in context: A165529 A116710 A165530 * A116704 A029759 A150255
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
STATUS
approved