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A005289 Number of graphs on n nodes with 3 cliques.
(Formerly M3440)
1

%I M3440

%S 0,0,1,4,12,31,67,132,239,407,657,1019,1523,2211,3126,4323,5859,7806,

%T 10236,13239,16906,21346,26670,33010,40498,49290,59543,71438,85158,

%U 100913,118913,139398,162609,188817,218295,251349,288285

%N Number of graphs on n nodes with 3 cliques.

%D R. K. Guy, personal communication.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H R. K. Guy, <a href="/A005289/a005289.pdf">Letter to N. J. A. Sloane, Apr 1988</a>

%H R. K. Guy, <a href="https://www.jstor.org/stable/2318549">Monthly research problems, 1969-73</a>, Amer. Math. Monthly, 80 (1973), 1120-1128.

%H R. K. Guy, <a href="https://www.jstor.org/stable/2318257">Monthly research problems, 1969-75</a>, Amer. Math. Monthly, 82 (1975), 995-1004.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">1031 Generating Functions and Conjectures</a>, Université du Québec à Montréal, 1992.

%H K. B. Reid, <a href="https://doi.org/10.1112/jlms/s2-8.1.94">The number of graphs on N vertices with 3 cliques</a>, J. London Math. Soc. (2) 8 (1974), 94-98.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Clique.html">Clique.</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-4,2,2,2,-4,-1,3,-1)

%F 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

%p A005289p := proc(n)

%p n*(2*n^2+3*n-6)/72 ;

%p round(%) ;

%p end proc:

%p A005289 := proc(n)

%p if type(n,'even') then

%p n*(n^2-4)*(n^2-6)/240+A005289p(n) ;

%p else

%p n*(n^2-1)*(n^2-9)/240+A005289p(n) ;

%p end if;

%p end proc:

%p seq(A005289(n),n=1..40) ; # _R. J. Mathar_, Aug 23 2015

%t 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 *)

%K nonn,nice,easy

%O 1,4

%A _N. J. A. Sloane_

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Last modified July 9 16:50 EDT 2020. Contains 335545 sequences. (Running on oeis4.)