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A006897
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a(n) is the number of hierarchical linear models on n unlabeled factors allowing 2-way interactions (but no higher order interactions); or the number of unlabeled simple graphs with <= n nodes.
(Formerly M1153)
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8
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1, 2, 4, 8, 19, 53, 209, 1253, 13599, 288267, 12293435, 1031291299, 166122463891, 50668153831843, 29104823811067331, 31455590793615376099, 64032471295321173271027, 245999896624828253856990803, 1787823725042236528801735181651, 24639597076850046760911809226614419
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of isolated points over all simple unlabelled graphs with (n+1) nodes. - Geoffrey Critzer, Apr 14 2012
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REFERENCES
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R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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EXAMPLE
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a(2) = 4 includes the null graph G1 = [], G2 = [o], G3 = [o o], and G4 = [o-o].
a(3) = 8 includes the null graph G1 = [], G2 = [o], G3 = [o o], G4 = [o-o], G5 = [o o o], G6 = [o-o o], G7 = [o-o-o], and G8 = [triangle with three unlabeled nodes]. - Petros Hadjicostas, Apr 10 2020
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MAPLE
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b:= proc(n, i, l) `if`(n=0 or i=1, 1/n!*2^((p-> add(ceil((p[j]-1)/2)
+add(igcd(p[k], p[j]), k=1..j-1), j=1..nops(p)))([l[], 1$n])),
add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i))
end:
a:= proc(n) option remember; b(n$2, [])+`if`(n>0, a(n-1), 0) end:
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MATHEMATICA
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nn = 15; g = Sum[NumberOfGraphs[n] x^n, {n, 0, nn}]; CoefficientList[Series[g/(1 - x), {x, 0, nn}], x] (* Geoffrey Critzer, Apr 12 2012 *)
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CROSSREFS
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KEYWORD
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easy,nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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