login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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