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 A328509 Number of non-unimodal sequences of length n covering an initial interval of positive integers. 45
 0, 0, 0, 3, 41, 425, 4287, 45941, 541219, 7071501 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A sequence of integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence. LINKS MathWorld, Unimodal Sequence EXAMPLE The a(3) = 3 sequences are (2,1,2), (2,1,3), (3,1,2). The a(4) = 41 sequences: (1212) (2113) (2134) (2413) (3142) (3412) (1213) (2121) (2143) (3112) (3212) (4123) (1312) (2122) (2212) (3121) (3213) (4132) (1323) (2123) (2213) (3122) (3214) (4213) (1324) (2131) (2312) (3123) (3231) (4231) (1423) (2132) (2313) (3124) (3241) (4312) (2112) (2133) (2314) (3132) (3312) MATHEMATICA allnorm[n_]:=If[n<=0, {{}}, Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1]]; unimodQ[q_]:=Or[Length[q]<=1, If[q[[1]]<=q[[2]], unimodQ[Rest[q]], OrderedQ[Reverse[q]]]]; Table[Length[Select[Union@@Permutations/@allnorm[n], !unimodQ[#]&]], {n, 0, 5}] CROSSREFS Not requiring non-unimodality gives A000670. The complement appears to be counted by A007052. The case where the negation is not unimodal either is A332873. Unimodal compositions are A001523. Non-unimodal permutations are A059204. Non-unimodal compositions are A115981. Unimodal compositions covering an initial interval are A227038. Numbers whose unsorted prime signature is not unimodal are A332282. Covering partitions with unimodal run-lengths are A332577. Non-unimodal compositions covering an initial interval are A332743. Cf. A060223, A255906, A332281, A332284, A332639, A332672, A332834, A332870. Sequence in context: A322244 A181226 A159249 * A087544 A305667 A213378 Adjacent sequences: A328506 A328507 A328508 * A328510 A328511 A328512 KEYWORD nonn,more AUTHOR Gus Wiseman, Feb 19 2020 EXTENSIONS a(9) from Robert Price, Jun 19 2021 STATUS approved

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Last modified December 7 19:19 EST 2022. Contains 358669 sequences. (Running on oeis4.)