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A093374 Number of 1-2-3-avoiding permutations with exactly thrice the 1-3-2 pattern. 1

%I

%S 1,5,18,57,168,472,1280,3376,8704,22016,54784,134400,325632,780288,

%T 1851392,4354048,10158080,23527424,54132736,123797504,281542656,

%U 637009920,1434451968,3215982592,7180648448,15971909632,35399925760,78198603776,172201345024

%N Number of 1-2-3-avoiding permutations with exactly thrice the 1-3-2 pattern.

%H Colin Barker, <a href="/A093374/b093374.txt">Table of n, a(n) for n = 4..1000</a>

%H D. Callan, <a href="http://arXiv.org/abs/math.CO/0211380">A recursive bijective approach to counting permutations...</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8, -24, 32, -16).

%F a(n) = C(n-3, 1)2^(n-4) + C(n-3, 1)2^(n-5) + C(n-3, 2)2^(n-7) for n<4, a(n) = 0.

%F G.f.: x^4*(1 - 3*x + 2*x^2 + x^3) / (1 - 2*x)^4. Corrected by _Colin Barker_, Feb 13 2017

%F From _Colin Barker_, Feb 13 2017: (Start)

%F a(n) = 2^(n-8)*(-120 + 38*n - 3*n^2 + n^3) / 3 for n>3.

%F a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) for n>7.

%F (End)

%o (PARI) a(n)=if(n<4,0,2^(n-4)*binomial(n-3,1)+2^(n-5)*binomial(n-3,2)+2^(n-7)*binomial(n-4,3))

%o (PARI) Vec(x^4*(1 - 3*x + 2*x^2 + x^3) / (1 - 2*x)^4 + O(x^30)) \\ _Colin Barker_, Feb 13 2017

%K nonn,easy

%O 4,2

%A _Ralf Stephan_, Apr 28 2004

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Last modified April 18 14:46 EDT 2019. Contains 322209 sequences. (Running on oeis4.)