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A116728
Number of permutations of length n which avoid the patterns 321, 1243, 2134.
1
1, 2, 5, 12, 19, 26, 33, 40, 47, 54, 61, 68, 75, 82, 89, 96, 103, 110, 117, 124, 131, 138, 145, 152, 159, 166, 173, 180, 187, 194, 201, 208, 215, 222, 229, 236, 243, 250, 257, 264, 271, 278, 285, 292, 299, 306, 313, 320, 327, 334, 341, 348, 355, 362, 369
OFFSET
1,2
FORMULA
G.f.: x*(1 + 2*x^2 + 4*x^3) / (1 - x)^2.
For n >= 3, a(n) = 7*n - 16. - Franklin T. Adams-Watters, Sep 16 2006
a(n) = 2*a(n-1) - a(n-2) for n=4. - Colin Barker, Oct 24 2017
a(n) = A017041(n-3) for n > 2. - Georg Fischer, Oct 07 2018
E.g.f.: exp(x)*(7*x - 16) + 2*(x^2 + 5*x + 8). - Stefano Spezia, Oct 10 2022
MAPLE
t := taylor((4*x^3+2*x^2+1)*x/(x-1)^2, x, 51):seq(coeff(t, x, n), n=1..50); # Nathaniel Johnston, Apr 27 2011
PROG
(PARI) Vec(x*(1 + 2*x^2 + 4*x^3) / (1 - x)^2 + O(x^70)) \\ Colin Barker, Oct 24 2017
CROSSREFS
Cf. A017041.
Sequence in context: A131091 A356490 A336462 * A276478 A333558 A095306
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
STATUS
approved