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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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Last modified November 23 19:03 EST 2017. Contains 295128 sequences.