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 A225095 The number of new maxima over all length n sequences on {1,2,...,n}. 1
 0, 1, 5, 41, 444, 5979, 96375, 1810297, 38845520, 937702437, 25154615815, 742476758297, 23915618605956, 834831863473087, 31395048114431183, 1265451184688113105, 54426870391856267072, 2488054366709505840265, 120468464465317265258991, 6158924799179729969013985 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..150 EXAMPLE a(2) = 5 because in the length 2 sequences on {1,2}: (1',1), (1',2'), (2',1), (2',2) there are 5 new maxima indicated with '. MAPLE b:= proc(n, i) option remember; if i<2 then [i\$j=1..n]       else b(n, i-1); add([0\$t=1..j-1, add(%[h], h=1..j)+            (j-1)^(i-1), %[t]\$t=j+1..n], j=1..n) fi     end: a:= n-> add(i, i=b(n, n)): seq(a(n), n=0..25);  # Alois P. Heinz, Apr 28 2013 MATHEMATICA f[x_List]:=Length[Union[Rest[FoldList[Max, 0, x]]]]; Table[Total[Map[f, Tuples[Range[1, n], n]]], {n, 1, 6}] CROSSREFS Cf. A000254 (analogous sequence for permutations). Sequence in context: A259609 A083073 A115257 * A222081 A047735 A096364 Adjacent sequences:  A225092 A225093 A225094 * A225096 A225097 A225098 KEYWORD nonn AUTHOR Geoffrey Critzer, Apr 27 2013 EXTENSIONS More terms from Alois P. Heinz, Apr 28 2013 STATUS approved

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