A116756 - OEIS

A116756

Number of permutations of length n which avoid the patterns 1234, 3421, 4312.

1, 2, 6, 21, 70, 177, 333, 538, 792, 1095, 1447, 1848, 2298, 2797, 3345, 3942, 4588, 5283, 6027, 6820, 7662, 8553, 9493, 10482, 11520, 12607, 13743, 14928, 16162, 17445, 18777, 20158, 21588, 23067, 24595, 26172, 27798, 29473, 31197, 32970, 34792, 36663, 38583

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..43.

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 7.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

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

FORMULA

G.f.: x*(9*x^6-24*x^5-23*x^4-8*x^3-3*x^2+x-1)/(x-1)^3.

For n >= 5, a(n) = (49*n^2 - 325*n + 540)/2. - Franklin T. Adams-Watters, Sep 16 2006

MAPLE