A116815 Number of permutations of length n which avoid the patterns 1234, 1432, 3241.

1, 2, 6, 21, 70, 199, 502, 1232, 2962, 6970, 16138, 36982, 84083, 189918, 426722, 954884, 2129756, 4737382, 10514539, 23294911, 51533491, 113864171, 251330512, 554292891, 1221605912, 2690738608, 5923829534, 13036444247, 28679413033

Offset

1,2

Links

Table of n, a(n) for n=1..29.

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 10.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (3,-1,0,-2,-4,-1,2,3,1).

Formula

G.f.: x (2x^10 +4x^9 +9x^8 +9x^7 +4x^6 -18x^5 -15x^4 -5x^3 -x^2+x-1)/((x-1) (x^3+x^2+x-1) (x^5+3x^4+2x^3+x^2+x-1))

Maple

cn := [-1, 2, 0, -1, -7, -19, -19, 6, 12, 10, 4, 2] ;
p := add(cn[i]*x^(i-1), i=1..nops(cn)) ;
q := (x-1)*(x^5+3*x^4+2*x^3+x^2+x-1)*(x^3+x^2+x-1) ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ; # R. J. Mathar, Nov 07 2017

Mathematica

Join[{1, 2}, LinearRecurrence[{3, -1, 0, -2, -4, -1, 2, 3, 1}, {6, 21, 70, 199, 502, 1232, 2962, 6970, 16138}, 30]] (* Harvey P. Dale, Nov 18 2014 *)

Crossrefs

Sequence in context: A116756 A116813 A116765 * A116804 A116832 A116811

Adjacent sequences: A116812 A116813 A116814 * A116816 A116817 A116818

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved