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A079105
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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.
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5
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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
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OFFSET
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1,2
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COMMENTS
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Periodic with period 3 from a(15) onwards.
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LINKS
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Table of n, a(n) for n=1..45.
Joseph Myers, The minimum number of monotone subsequences, Electronic J. Combin. 9(2) (2002), #R4.
Index entries for linear recurrences with constant coefficients, signature (0, 0, 1).
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FORMULA
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A079102, A079103, A079104, A079106.
Sequence in context: A150254 A148497 A206736 * A079104 A116705 A116708
Adjacent sequences: A079102 A079103 A079104 * A079106 A079107 A079108
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KEYWORD
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nonn,easy
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AUTHOR
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Joseph Myers, Dec 23 2002
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STATUS
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approved
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