A116842 Number of permutations of length n which avoid the patterns 1234, 2143, 3421.

1, 2, 6, 21, 69, 181, 375, 651, 1009, 1449, 1971, 2575, 3261, 4029, 4879, 5811, 6825, 7921, 9099, 10359, 11701, 13125, 14631, 16219, 17889, 19641, 21475, 23391, 25389, 27469

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 3.

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) = -{x(18x^6+31x^5+22x^4+8x^3+3x^2-x+1)}/(x-1)^3.

FOr n >= 5, a(n) = 41n^2 - 339n + 739. - Franklin T. Adams-Watters, Sep 16 2006

Maple

cn := [1, -2, 2, 2, 8, 22, 31, 18] ;
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: A119098 A294706 A294707 * A294708 A294709 A116774

Adjacent sequences: A116839 A116840 A116841 * A116843 A116844 A116845

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved