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%I #5 Feb 14 2017 12:05:25
%S 0,0,2,15,75,313,1179,4161,14051,45993,147195,463345,1440723,4438905,
%T 13582955,41350977,125404611,379228489,1144370139,3447856017,
%U 10375942835,31198607385,93749962827,281584384225,845476670115,2537990291433,7617326317499
%N Number of permutations with exactly 1 valley which avoid the pattern 1324.
%H Colin Barker, <a href="/A099743/b099743.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (9,-30,44,-24).
%F G.f.: (2-3*x)*x^3 / ((1-2*x)^3*(1-3*x)).
%F From _Colin Barker_, Feb 14 2017: (Start)
%F a(n) = -7*2^(n-3) + 3^n - 9*2^(n-4)*n - 2^(n-4)*n^2.
%F a(n) = 9*a(n-1) - 30*a(n-2) + 44*a(n-3) - 24*a(n-4) for n>4.
%F (End)
%e a(3) = 2 because 213 and 312 have exactly 1 valley and avoid 1324.
%o (PARI) concat(vector(2), Vec(x^3*(2-3*x) / ((1-2*x)^3*(1-3*x)) + O(x^30))) \\ _Colin Barker_, Feb 14 2017
%Y Cf. A000079.
%K nonn,easy
%O 1,3
%A _Mike Zabrocki_, Nov 09 2004
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