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A054558
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Number of labeled pure 2-complexes on n nodes (0-simplexes) with 5 2-simplexes and 9 1-simplexes.
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1
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150, 960, 3605, 10360, 25200, 54600, 108570, 201960, 356070, 600600, 975975, 1536080, 2351440, 3512880, 5135700, 7364400, 10377990, 14395920, 19684665, 26565000, 35420000, 46703800, 60951150, 78787800, 100941750, 128255400
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OFFSET
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5,1
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COMMENTS
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Number of {T_1,T_2,...,T_k} where T_i, i=1..k are 3-subsets of an n-set such that {D | D is 2-subset of T_i for some i=1..k} has l elements; k=5, l=9.
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REFERENCES
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V. Jovovic, On the number of two-dimensional simplicial complexes (in Russian), Metody i sistemy tekhnicheskoy diagnostiki, Vypusk 16, Mezhvuzovskiy zbornik nauchnykh trudov, Izdatelstvo Saratovskogo universiteta, 1991.
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LINKS
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FORMULA
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a(n) = 150*C(n,5) +60*C(n,6) +35*C(n,7) = n*(n-1)*(n-2)*(n-3)*(n-4)*(n^2+n+150)/144.
G.f.: 5*x^5*(30-48*x+25*x^2)/(1-x)^8. - Colin Barker, Jun 21 2012
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MAPLE
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MATHEMATICA
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Table[n*(n - 1)*(n - 2)*(n - 3)*(n - 4)*(n^2 + n + 150)/144, {n, 5, 30}] (* Wesley Ivan Hurt, Apr 29 2014 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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