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Search: id:A125183
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| A125183 |
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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). |
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+0
1
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| 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
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OFFSET
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1,2
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COMMENT
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Row sums are the factorial numbers (A000142). T(n,n)=A075866(n). In the Maple program define n (<=10) to obtain row n.
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EXAMPLE
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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,
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MAPLE
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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)
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CROSSREFS
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Cf. A000142, A075866.
Sequence in context: A112899 A108263 A134433 this_sequence A092583 A079134 A112340
Adjacent sequences: A125180 A125181 A125182 this_sequence A125184 A125185 A125186
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 24 2006
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