A116765 Number of permutations of length n which avoid the patterns 1234, 2431, 4312.

1, 2, 6, 21, 70, 195, 458, 942, 1752, 3016, 4886, 7539, 11178, 16033, 22362, 30452, 40620, 53214, 68614, 87233, 109518, 135951, 167050, 203370, 245504, 294084, 349782, 413311, 485426, 566925, 658650, 761488, 876372, 1004282, 1146246, 1303341, 1476694, 1667483

Offset

1,2

Links

Table of n, a(n) for n=1..38.

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 9.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

G.f.: -x*(3*x^6+6*x^5-9*x^4+5*x^3-9*x^2+4*x-1)/(x-1)^6.

For n >= 2, a(n) = (n^5 + 75*n^4 - 715*n^3 + 2685*n^2 - 4446*n + 2880)/120. - Franklin T. Adams-Watters, Sep 16 2006

Maple

cn := [1, -5, 11, -11, 10, 3, -5, -3] ;
p := add(cn[i]*x^(i-1), i=1..nops(cn)) ;
q := (1-x)^6 ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ; # R. J. Mathar, Nov 07 2017

Crossrefs

Sequence in context: A116774 A116756 A116813 * A116815 A116804 A116832

Adjacent sequences: A116762 A116763 A116764 * A116766 A116767 A116768

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Extensions

More terms from Jason Yuen, Sep 17 2025

Status

approved