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%I #18 Mar 15 2024 10:12:27
%S 3,6,17,42,102,242,564,1296,2944,6624,14784,32768,72192,158208,345088,
%T 749568,1622016,3497984,7520256,16121856,34471936,73531392,156499968,
%U 332398592,704643072,1491075072,3149922304,6643777536,13992198144
%N Number of permutations of length n containing exactly once 132 and 213, likewise for pattern pair (231,312).
%H Aaron Robertson, <a href="https://arxiv.org/abs/math/0012029">Permutations restricted by two distinct patterns of length three</a>, arXiv:math/0012029 [math.CO], 2000.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).
%F For n>=7, a(n) = (n^2+21*n-28)*2^(n-9).
%F G.f.: x^4*(x-1)^2*(2*x^3-2*x^2+6*x-3) / (2*x-1)^3. [_Colin Barker_, Jan 31 2013]
%t LinearRecurrence[{6,-12,8},{3,6,17,42,102,242},40] (* _Harvey P. Dale_, Apr 10 2022 *)
%Y Cf. A001815.
%K nonn,easy
%O 4,1
%A _Ralf Stephan_, Oct 30 2003
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