A147681 - OEIS

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

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OFFSET

0,4

COMMENTS

Same as A145874.

LINKS

Table of n, a(n) for n=0..27.

David Scambler et al., A147681 Late-growing permutations and follow-up messages on the SeqFan list, Aug 10 2012

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 *)

CROSSREFS

This is the first of 19 related sequences, the others being A147682, A147684, A147686, A147687, A147692, A147694, A147695, A147697, A147698, A147700, A147705, A147707, A147712, A147713, A147714, A147715, A147717, A147769.

Column k=1 of A215561.

Sequence in context: A336012 A212417 A145874 * A055487 A121130 A006099

Adjacent sequences: A147678 A147679 A147680 * A147682 A147683 A147684

KEYWORD

nonn,hard

AUTHOR

R. H. Hardin, May 01 2009

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

STATUS

approved