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A144208
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Number of simple graphs on n labeled nodes, where each maximally connected subgraph consists of a single node or has a unique cycle of length 3; also row sums of A144207.
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3
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1, 1, 1, 2, 17, 221, 3261, 54801, 1049235, 22695027, 548904831, 14701691121, 432342705351, 13856514927207, 480891887472585, 17971038945463101, 719613541474095591, 30743125693699501431, 1395902175504288127695
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OFFSET
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0,4
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..150
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FORMULA
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a(n) = Sum_{k=0..n} A144207(n,k).
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EXAMPLE
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a(3) = 2, because there are 2 simple graphs on 3 labeled nodes, where each maximally connected subgraph consists of a single node or has a unique cycle of length 3:
.1.2. .1-2.
..... .|/..
.3... .3...
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MAPLE
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T:= proc(n, k) option remember; if k=0 then 1 elif k<0 or n<k then 0 elif k=n then binomial (n-1, 2) *n^(n-3) else T(n-1, k) +add (binomial (n-1, j) * T(j+1, j+1) *T(n-1-j, k-j-1), j=2..k-1) fi end: a:= n-> add (T(n, k), k=0..n): seq (a(n), n=0..23);
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CROSSREFS
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Row sums of triangle A144207. A column of A144212. Cf. A053507, A007318.
Sequence in context: A126752 A004029 A114268 * A183711 A058239 A006227
Adjacent sequences: A144205 A144206 A144207 * A144209 A144210 A144211
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Sep 14 2008
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STATUS
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approved
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