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Search: id:A144151
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| A144151 |
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Triangle T(n,k), n>=0, 0<=k<=n, read by rows: T(n,k) = number of ways an undirected cycle of length k can be built from n labeled nodes. |
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8
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| 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 3, 1, 5, 10, 10, 15, 12, 1, 6, 15, 20, 45, 72, 60, 1, 7, 21, 35, 105, 252, 420, 360, 1, 8, 28, 56, 210, 672, 1680, 2880, 2520, 1, 9, 36, 84, 378, 1512, 5040, 12960, 22680, 20160, 1, 10, 45, 120, 630, 3024, 12600, 43200, 113400
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OFFSET
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0,5
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FORMULA
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T(n,k)=C(n,k) if k<=2, else T(n,k)=C(n,k)*(k-1)!/2.
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EXAMPLE
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T(4,3)=4, because 4 undirected cycles of length 3 can be built from 4 labeled nodes:
.1.2. .1.2. .1-2. .1-2.
../|. .|\.. ..\|. .|/..
.3-4. .3-4. .3.4. .3.4.
Triangle begins:
1
1, 1
1, 2, 1
1, 3, 3, 1
1, 4, 6, 4, 3
1, 5, 10, 10, 15, 12
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MAPLE
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T:= (n, k)-> if k<=2 then binomial(n, k) else product (n-j, j=0..k-1)/k/2 fi: seq (seq (T(n, k), k=0..n), n=0..12);
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CROSSREFS
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Columns 0-4 give: A000012, A000027, A000217, A000292, A050534. Diagonal gives: A001710. Cf. A000142, A007318.
Row sums are in A116723. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jun 01 2009]
Sequence in context: A118687 A026022 A073714 this_sequence A022818 A050447 A167172
Adjacent sequences: A144148 A144149 A144150 this_sequence A144152 A144153 A144154
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KEYWORD
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nonn,tabl
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 12 2008
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