A294764 Number of permutations of [n] avoiding {2143, 3142, 1234}.

1, 1, 2, 6, 21, 73, 247, 821, 2704, 8868, 29030, 94960, 310531, 1015359, 3319829, 10854379, 35488838, 116031978, 379370276, 1240362982, 4055405209, 13259272613, 43351600979, 141739396705, 463421329340, 1515170329456, 4953896123490, 16196916164572, 52956316947055, 173142311541835

Offset: 0

Author

R. J. Mathar, Nov 08 2017

Keywords

• nonn
• easy

Links

• D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 [math.CO] (2017), Table 2 No 111.
• Index entries for linear recurrences with constant coefficients, signature (7,-18,24,-19,9,-2).

Programs

Maple

((x^3-2*x^2+3*x-1)^2)/((2*x^3-3*x^2+4*x-1)*(x-1)^3) ;
taylor(%,x=0,40) ;
gfun[seriestolist](%) ;

Formula

4*a(n) = n+1-n^2 -A175005(n) +A175005(n+1), n>0. - R. J. Mathar, Nov 05 2021