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A125183 Triangle read by rows: T(n,k) is the number of permutations p of {1,2,...,n} such that the set {|p(i)-i|, i=1,2,...,n} has exactly k elements (1<=k<=n). 0
1, 2, 0, 1, 5, 0, 3, 11, 6, 4, 1, 28, 55, 32, 4, 3, 69, 210, 330, 108, 0, 1, 102, 846, 2177, 1590, 324, 0, 4, 279, 2694, 11221, 17578, 7624, 888, 32, 1, 328, 7791, 54777, 135993, 123474, 37524, 2896, 96, 3, 961, 24032, 227906, 914364, 1427342, 839904, 182824, 11464, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums are the factorial numbers (A000142). T(n,n) = A075866(n). In the Maple program define n (<=10) to obtain row n.

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

T(4,3)=6 because we have 1423, 1342, 3124, 4312, 2314 and 3421.

Triangle starts:

1;

2,  0;

1,  5,   0;

3, 11,   6,   4;

1, 28,  55,  32,   4;

3, 69, 210, 330, 108,  0;

MAPLE

n:=7: with(combinat): P:=permute(n): for j from 1 to n! do c[j]:=0 od: for j from 1 to n! do if nops({seq(abs(P[j][i]-i), i=1..n)}) = 1 then c[1]:=c[1]+1 elif nops({seq(abs(P[j][i]-i), i=1..n)}) = 2 then c[2]:=c[2]+1 elif nops({seq(abs(P[j][i]-i), i=1..n)}) = 3 then c[3]:=c[3]+1 elif nops({seq(abs(P[j][i]-i), i=1..n)}) = 4 then c[4]:=c[4]+1 elif nops({seq(abs(P[j][i]-i), i=1..n)}) = 5 then c[5]:=c[5]+1 elif nops({seq(abs(P[j][i]-i), i=1..n)}) = 6 then c[6]:=c[6]+1 elif nops({seq(abs(P[j][i]-i), i=1..n)}) = 7 then c[7]:=c[7]+1 elif nops({seq(abs(P[j][i]-i), i=1..n)}) = 8 then c[8]:=c[8]+1 elif nops({seq(abs(P[j][i]-i), i=1..n)}) = 9 then c[9]:=c[9]+1 elif nops({seq(abs(P[j][i]-i), i=1..n)}) = 10 then c[10]:=c[10]+1 else fi od: seq(c[i], i=1..n); # yields row n for the specified n (n<=10)

CROSSREFS

Cf. A000142, A075866.

Sequence in context: A108263 A244523 A134433 * A092583 A285212 A262948

Adjacent sequences:  A125180 A125181 A125182 * A125184 A125185 A125186

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Nov 24 2006

STATUS

approved

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Last modified October 21 23:02 EDT 2018. Contains 316431 sequences. (Running on oeis4.)