A147681 Late-growing permutations: number of permutations of 1..n with every partial sum <= the same partial sum averaged over all permutations.
1, 1, 1, 3, 7, 35, 139, 1001, 5701, 53109, 402985, 4605271, 43665667, 589809987, 6735960079, 104899483845, 1402547616085, 24698838710457, 378845419610773, 7444522779300351, 128830635114146047, 2792467448952670671, 53854927962971227495, 1276369340371154144337, 27141331409803338993193, 698008560075731437652425, 16228797258964121571885457, 450111715263775132783135875
Offset: 0
Links
- David Scambler et al., A147681 Late-growing permutations and follow-up messages on the SeqFan list, Aug 10 2012
Crossrefs
Programs
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Maple
a:= proc(n) option remember; local b, m; m:= n*(n+1)/2; b:= proc(s) option remember; local h, g; h:= nops(s); g:= (n-h+1)*(1+n)/2 -m +add(i, i=s); `if`(h<2, 1, add(`if`(s[i]<=g, b(subsop(i=NULL, s)), 0), i=1..h)) end; forget(b); b([$1..n]) end: seq(a(n), n=0..15); # Alois P. Heinz, Aug 10 2012 -
Mathematica
a[n_] := a[n] = Module[{b, m}, m = n*(n+1)/2; b[s_List] := b[s] = Module[{h, g}, h = Length[s]; g = (n-h+1)*(1+n)/2 - m + Total[s]; If[h<2, 1, Sum[If[s[[i]] <= g, b[ReplacePart[s, i -> Sequence[]]], 0], {i, 1, h}]]]; b[Range[n]]]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Mar 13 2015, after Alois P. Heinz *)
Extensions
a(22) from Alois P. Heinz, Aug 10 2012
a(23) from Alois P. Heinz, Nov 01 2014
a(24)-a(25) from Vaclav Kotesovec, Jan 31 2015
a(26)-a(27) from Vaclav Kotesovec, Sep 07 2016
Comments