login
A116711
Number of permutations of length n which avoid the patterns 123, 3214, 4312.
3
1, 2, 5, 12, 23, 36, 51, 68, 87, 108, 131, 156, 183, 212, 243, 276, 311, 348, 387, 428, 471, 516, 563, 612, 663, 716, 771, 828, 887, 948, 1011, 1076, 1143, 1212, 1283, 1356, 1431, 1508, 1587, 1668, 1751, 1836, 1923, 2012, 2103, 2196, 2291, 2388, 2487, 2588
OFFSET
1,2
FORMULA
G.f.: x*(1 - x + 2*x^2 + 2*x^3 - 2*x^5) / (1 - x)^3.
For n >= 4, a(n) = n^2 + 2*n - 12. - Franklin T. Adams-Watters, Sep 16 2006
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3. - Colin Barker, Oct 23 2017
PROG
(PARI) Vec(x*(1 - x + 2*x^2 + 2*x^3 - 2*x^5) / (1 - x)^3 + O(x^50)) \\ Colin Barker, Oct 23 2017
CROSSREFS
Sequence in context: A123647 A166249 A326762 * A247658 A109653 A115520
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
STATUS
approved