A116756 Number of permutations of length n which avoid the patterns 1234, 3421, 4312.

1, 2, 6, 21, 70, 177, 333, 538, 792, 1095, 1447, 1848, 2298, 2797, 3345, 3942, 4588, 5283, 6027, 6820, 7662, 8553, 9493, 10482, 11520, 12607, 13743, 14928, 16162, 17445

Offset

1,2

Links

Table of n, a(n) for n=1..30.

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 7.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.: A(x) = {(9x^6-24x^5-23x^4-8x^3-3x^2+x-1)x}/{(x-1)^3}

For n >= 5, a(n) = (49n^2 - 325n + 540)/2. - Franklin T. Adams-Watters, Sep 16 2006

Maple

cn := [1, -2, 2, 2, 8, 23, 24, -9] ;
p := add(cn[i]*x^(i-1), i=1..nops(cn)) ;
q := (1-x)^3 ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ; # R. J. Mathar, Nov 07 2017

Crossrefs

Sequence in context: A294708 A294709 A116774 * A116813 A116765 A116815

Adjacent sequences: A116753 A116754 A116755 * A116757 A116758 A116759

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved