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A005289 Number of graphs on n nodes with 3 cliques.
(Formerly M3440)
1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

REFERENCES

R. K. Guy, personal communication.

R. K. Guy, Monthly research problems, 1969-73, Amer. Math. Monthly, 80 (1973), 1120-1128.

R. K. Guy, Monthly research problems, 1969-75, Amer. Math. Monthly, 82 (1975), 995-1004.

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

LINKS

Table of n, a(n) for n=1..37.

R. K. Guy, Letter to N. J. A. Sloane, Apr 1988

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Reid, K. B. The number of graphs on N vertices with 3 cliques, J. London Math. Soc. (2) 8 (1974), 94-98.

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)

FORMULA

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

MAPLE

A005289p := proc(n)

    n*(2*n^2+3*n-6)/72 ;

    round(%) ;

end proc:

A005289 := proc(n)

    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:

seq(A005289(n), n=1..40) ; # R. J. Mathar, Aug 23 2015

MATHEMATICA

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 *)

CROSSREFS

Sequence in context: A297079 A074210 A299053 * A037255 A027658 A001982

Adjacent sequences:  A005286 A005287 A005288 * A005290 A005291 A005292

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 17 18:46 EST 2019. Contains 320222 sequences. (Running on oeis4.)