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A079105
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.
5
1, 2, 6, 22, 86, 306, 882, 1764, 1764, 8738, 6892, 1682, 4614, 4182, 1250, 3750, 3750, 1250, 3750, 3750, 1250, 3750, 3750, 1250, 3750, 3750, 1250, 3750, 3750, 1250, 3750, 3750, 1250, 3750, 3750, 1250, 3750, 3750, 1250, 3750, 3750, 1250, 3750, 3750, 1250
OFFSET
1,2
COMMENTS
Periodic with period 3 from a(15) onwards.
FORMULA
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
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Joseph Myers, Dec 23 2002
STATUS
approved