A116833 Number of permutations of length n which avoid the patterns 2134, 3421, 4132.

1, 2, 6, 21, 71, 213, 564, 1340, 2909, 5860, 11090, 19911, 34179, 56447, 90144, 139782, 211193, 311798, 450910, 640073, 893439, 1228185, 1664972, 2228448, 2947797, 3857336, 4997162, 6413851, 8161211, 10301091, 12904248, 16051274, 19833585, 24354474, 29730230

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 26.

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) = -x*(2x^7-8x^6+19x^5-29x^4+27x^3-18x^2+6x-1)/(x-1)^8.

a(n) = (n^7 + 7*n^6 - 56*n^5 + 490*n^4 - 2051*n^3 + 5803*n^2 - 6714*n + 5040)/2520. - Franklin T. Adams-Watters, Sep 16 2006

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n > 8. - Wesley Ivan Hurt, Oct 09 2017

Maple

A116833:=n->(n^7 + 7*n^6 - 56*n^5 + 490*n^4 - 2051*n^3 + 5803*n^2 - 6714*n + 5040)/2520: seq(A116833(n), n=1..50); # Wesley Ivan Hurt, Oct 09 2017

Mathematica

CoefficientList[Series[-(2 x^7 - 8 x^6 + 19 x^5 - 29 x^4 + 27 x^3 - 18 x^2 + 6 x - 1)/(1 - x)^8, {x, 0, 50}], x] (* Wesley Ivan Hurt, Oct 09 2017 *)

Prog

(Magma) [(n^7 + 7*n^6 - 56*n^5 + 490*n^4 - 2051*n^3 + 5803*n^2 - 6714*n + 5040)/2520 : n in [1..50]]; // Wesley Ivan Hurt, Oct 09 2017

Crossrefs

Sequence in context: A116835 A294725 A116755 * A116808 A294726 A294700

Adjacent sequences: A116830 A116831 A116832 * A116834 A116835 A116836

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved