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A116833
Number of permutations of length n which avoid the patterns 2134, 3421, 4132.
1
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
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
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
STATUS
approved