A116818 Number of permutations of length n which avoid the patterns 1234, 2341, 3421.

1, 2, 6, 21, 75, 248, 735, 1952, 4697, 10378, 21320, 41163, 75363, 131808, 221561, 359742, 566561, 868514, 1299754, 1903649, 2734539, 3859704, 5361555, 7340060, 9915417, 13230986, 17456492, 22791511, 29469251, 37760640

Offset

1,2

Links

Table of n, a(n) for n=1..30.

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 143.

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.: A(x) = -{(2x^7-11x^6+16x^5-33x^4+27x^3-18x^2+6x-1)x}/{(x-1)^8}

a(n) = (12n^7 - 119n^6 + 651n^5 - 1505n^4 + 693n^3 + 6664n^2 - 11436n + 10080)/5040. - Franklin T. Adams-Watters, Sep 16 2006

Mathematica

LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 2, 6, 21, 75, 248, 735, 1952}, 40] (* Harvey P. Dale, Apr 01 2019 *)

Crossrefs

Sequence in context: A360151 A150186 A150187 * A294770 A116763 A116840

Adjacent sequences: A116815 A116816 A116817 * A116819 A116820 A116821

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved