|
%I #10 Aug 25 2015 16:36:55
%S 1,2,6,22,86,306,882,1764,1764,8738,6892,1682,4614,4182,1250,3750,
%T 3750,1250,3750,3750,1250,3750,3750,1250,3750,3750,1250,3750,3750,
%U 1250,3750,3750,1250,3750,3750,1250,3750,3750,1250,3750,3750,1250,3750,3750,1250
%N Number of permutations of length n, in which all monotone subsequences of length 4 are descending or all such subsequences are ascending, containing the minimum number of such subsequences subject to that constraint.
%C Periodic with period 3 from a(15) onwards.
%H Joseph Myers, <a href="http://www.combinatorics.org/Volume_9/Abstracts/v9i2r4.html">The minimum number of monotone subsequences</a>, Electronic J. Combin. 9(2) (2002), #R4.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 1).
%F G.f.: x*(432*x^16 +864*x^15 +432*x^14 +2710*x^13 +4124*x^12 +82*x^11 -5128*x^10 -7856*x^9 -1458*x^8 -1678*x^7 -860*x^6 -300*x^5 -84*x^4 -21*x^3 -6*x^2 -2*x -1) / ((x -1)*(x^2 +x +1)). - _Colin Barker_, Jul 06 2013
%t Join[{1, 2, 6, 22, 86, 306, 882, 1764, 1764, 8738, 6892, 1682, 4614, 4182},LinearRecurrence[{0, 0, 1},{1250, 3750, 3750},31]] (* _Ray Chandler_, Aug 25 2015 *)
%Y Cf. A079102, A079103, A079104, A079106.
%K nonn,easy
%O 1,2
%A _Joseph Myers_, Dec 23 2002
|
