A116791 Number of permutations of length n which avoid the patterns 1234, 1342, 4312.

1, 2, 6, 21, 72, 220, 590, 1409, 3055, 6118, 11474, 20373, 34542, 56304, 88714, 135713, 202301, 294730, 420718, 589685, 813012, 1104324, 1479798, 1958497, 2562731, 3318446, 4255642, 5408821, 6817466, 8526552, 10587090, 13056705, 16000249, 19490450, 23608598

Offset

1,2

Links

Table of n, a(n) for n=1..35.

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 41.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

G.f.: -x*(x^7-6*x^6+20*x^5-30*x^4+27*x^3-18*x^2+6*x-1)/(x-1)^8.

a(n) = (n^7 + 35*n^6 - 203*n^5 + 665*n^4 - 686*n^3 + 1820*n^2 - 1632*n + 5040)/5040. - Franklin T. Adams-Watters, Sep 16 2006

Crossrefs

Sequence in context: A294753 A294754 A116750 * A116775 A116786 A116748

Adjacent sequences: A116788 A116789 A116790 * A116792 A116793 A116794

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Extensions

More terms from Jason Yuen, Sep 17 2025

Status

approved