A116804 Number of permutations of length n which avoid the patterns 1234, 1432, 4231.

1, 2, 6, 21, 70, 200, 481, 1004, 1886, 3270, 5325, 8246, 12254, 17596, 24545, 33400, 44486, 58154, 74781, 94770, 118550, 146576, 179329, 217316, 261070, 311150, 368141, 432654, 505326, 586820

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 11.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1)

Formula

G.f.: A(x) = -{x(5x^8-2x^7-x^6+9x^5+10x^4+x^3+6x^2-3x+1)}/{(x-1)^5}

For n >= 5, a(n) = (13n^4 - 156n^3 + 893n^2 - 2790n + 3840)/12. - Franklin T. Adams-Watters, Sep 16 2006

Maple

cn := [1, -4, 7, -4, 6, 9, 9, -1, -2, 5] ;
p := add(cn[i]*x^(i-1), i=1..nops(cn)) ;
q := (1-x)^5 ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ; # R. J. Mathar, Nov 07 2017

Crossrefs

Sequence in context: A116813 A116765 A116815 * A116832 A116811 A294718

Adjacent sequences: A116801 A116802 A116803 * A116805 A116806 A116807

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved