A225095 The number of new maxima over all length n sequences on {1,2,...,n}.

0, 1, 5, 41, 444, 5979, 96375, 1810297, 38845520, 937702437, 25154615815, 742476758297, 23915618605956, 834831863473087, 31395048114431183, 1265451184688113105, 54426870391856267072, 2488054366709505840265, 120468464465317265258991, 6158924799179729969013985

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

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), A336482.

Sequence in context: A323213 A083073 A115257 * A302100 A222081 A047735

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