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A055484 Number of unlabeled 3-element intersecting families (with not necessarily distinct sets) of an n-element set.

%I A055484 #20 Jul 02 2025 16:01:59
%S A055484 1,4,14,39,96,213,437,837,1520,2632,4380,7040,10979,16668,24716,35879,
%T A055484 51104,71549,98625,134025,179782,238292,312386,405368,521083,663968,
%U A055484 839140,1052439,1310534,1620985,1992343,2434229,2957458,3574108
%N A055484 Number of unlabeled 3-element intersecting families (with not necessarily distinct sets) of an n-element set.
%H A055484 G. C. Greubel, <a href="/A055484/b055484.txt">Table of n, a(n) for n = 1..1000</a>
%H A055484 V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.4213/dm398">On the number of Boolean functions in the Post classes F^{mu}_8</a>, (in Russian), Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
%H A055484 V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.1515/dma.1999.9.6.593">On the number of Boolean functions in the Post classes F^{mu}_8</a>, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.
%H A055484 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (4, -4, -2, 2, 4, 3, -12, 3, 4, 2, -2, -4, 4, -1).
%F A055484 G.f.: -x*(x^3-x^2-1)*(x^6+x^4+2*x^3+x^2+1)/((x^3-1)^2*(x^2-1)^2*(x-1)^4).
%t A055484 Rest[CoefficientList[Series[-x*(x^3 - x^2 - 1)*(x^6 + x^4 + 2*x^3 + x^2 + 1)/((x^3 - 1)^2*(x^2 - 1)^2*(x - 1)^4), {x, 0, 50}], x]] (* _G. C. Greubel_, Oct 06 2017 *)
%t A055484 LinearRecurrence[{4,-4,-2,2,4,3,-12,3,4,2,-2,-4,4,-1},{1,4,14,39,96,213,437,837,1520,2632,4380,7040,10979,16668},40] (* _Harvey P. Dale_, Jun 10 2024 *)
%o A055484 (PARI) x='x+O('x^50); Vec(-x*(x^3-x^2-1)*(x^6+x^4+2*x^3+x^2+1)/( (x^3-1)^2*(x^2-1)^2*(x-1)^4)) \\ _G. C. Greubel_, Oct 06 2017
%Y A055484 Cf. A053155 (labeled case), A005783, A002727, A051180.
%K A055484 nonn
%O A055484 1,2
%A A055484 _Vladeta Jovovic_, Goran Kilibarda, Jul 03 2000
%E A055484 More terms from _James Sellers_, Jul 04 2000