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A327904
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Number of labeled simple graphs with vertices {1..n} such that every edge has a different sum.
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2
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1, 1, 2, 8, 48, 432, 5184, 82944, 1658880, 41472000, 1244160000, 44789760000, 1881169920000, 92177326080000, 5161930260480000, 330363536670720000, 23786174640291840000, 1926680145863639040000, 173401213127727513600000, 17340121312772751360000000
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Product_{k=1..2*n+1} ceiling(k/4). - Andrew Howroyd, Oct 02 2019
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EXAMPLE
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The graph with edge-set {{1,2},{1,3},{1,4},{2,3}}, which looks like a triangle with a tail, has edges {1,4} and {2,3} with equal sum, so is not counted under a(4).
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1,
a(n-1)*ceil(n/2)*ceil(n/2+1/4))
end:
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MATHEMATICA
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stableSets[u_, Q_]:=If[Length[u]==0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r==w||Q[r, w]||Q[w, r]], Q]]]];
qes[n_]:=stableSets[Subsets[Range[n], {2}], Total[#1]==Total[#2]&];
Table[Length[qes[n]], {n, 0, 5}]
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PROG
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(PARI) a(n) = {prod(k=1, 2*n+1, ceil(k/4))} \\ Andrew Howroyd, Oct 02 2019
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CROSSREFS
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The generalization to antichains is A326030.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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