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A144210
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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 4; also row sums of A144209.
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2
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1, 1, 1, 1, 4, 76, 1486, 29506, 628531, 14633011, 373486051, 10423892971, 316702467496, 10422938835196, 369779598658786, 14078057663869606, 572776958092098166, 24810200300393961286, 1140218754844983978646
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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FORMULA
| a(n) = Sum_{k=0..n} A144209(n,k).
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EXAMPLE
| a(4) = 4, because there are 4 simple graphs on 4 labeled nodes, where each maximally connected subgraph consists of a single node or has a unique cycle of length 4:
.1.2. .1-2. .1-2. .1.2.
..... .|.|. ..X.. .|X|.
.3.4. .3-4. .3-4. .3.4.
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MAPLE
| T:= proc(n, k) option remember; if k=0 then 1 elif k<0 or n<k then 0 elif k=n then > 3*binomial (n-1, 3)*n^(n-4) else T(n-1, k) +add (binomial (n-1, j) * T(j+1, j+1) *T(n-1-j, k-j-1), j=3..k-1) fi end: a:= n-> add (T(n, k), k=0..n): seq (a(n), n=0..23);
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CROSSREFS
| A column of A144212. Cf. A144209.
Sequence in context: A190395 A114453 A093184 * A187542 A009631 A012020
Adjacent sequences: A144207 A144208 A144209 * A144211 A144212 A144213
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KEYWORD
| nonn
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 14 2008
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