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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Periodic with period 3 from a(15) onwards.

LINKS

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).

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

Cf. A079102, A079103, A079104, A079106.

Sequence in context: A150254 A148497 A206736 * A079104 A116705 A116708

Adjacent sequences:  A079102 A079103 A079104 * A079106 A079107 A079108

KEYWORD

nonn,easy

AUTHOR

Joseph Myers, Dec 23 2002

STATUS

approved

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Last modified July 19 03:54 EDT 2019. Contains 325144 sequences. (Running on oeis4.)