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A005289
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Number of graphs on n nodes with 3 cliques.
(Formerly M3440)
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1
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0, 0, 1, 4, 12, 31, 67, 132, 239, 407, 657, 1019, 1523, 2211, 3126, 4323, 5859, 7806, 10236, 13239, 16906, 21346, 26670, 33010, 40498, 49290, 59543, 71438, 85158, 100913, 118913, 139398, 162609, 188817, 218295, 251349, 288285
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listen;
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OFFSET
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1,4
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REFERENCES
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R. K. Guy, personal communication.
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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Eric Weisstein's World of Mathematics, Clique.
Index entries for linear recurrences with constant coefficients, signature (3,-1,-4,2,2,2,-4,-1,3,-1)
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FORMULA
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G.f.: x^3*(1+x+3*x^3+x^2) / ( (1+x+x^2)*(1+x)^2*(x-1)^6 ). - Simon Plouffe in his 1992 dissertation
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MAPLE
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A005289p := proc(n)
n*(2*n^2+3*n-6)/72 ;
round(%) ;
end proc:
if type(n, 'even') then
n*(n^2-4)*(n^2-6)/240+A005289p(n) ;
else
n*(n^2-1)*(n^2-9)/240+A005289p(n) ;
end if;
end proc:
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MATHEMATICA
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s = x^2*(3*x^3+x^2+x+1) / ((x-1)^6*(x+1)^2*(x^2+x+1)) + O[x]^40; CoefficientList[s, x] (* Jean-François Alcover, Nov 27 2015 *)
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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