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%I #38 Sep 08 2022 08:45:00
%S 0,2,9,32,105,332,1029,3152,9585,29012,87549,263672,793065,2383292,
%T 7158069,21490592,64504545,193579172,580868589,1742867912,5229128025,
%U 15688432652,47067395109,141206379632,423627527505,1270899359732,3812731633629,11438262009752
%N Number of 2-element intersecting families whose union is an n-element set.
%H G. C. Greubel, <a href="/A053152/b053152.txt">Table of n, a(n) for n = 1..1000</a>
%H V. Jovovic and 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 V. Jovovic and 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 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F a(n) = (1/2!)*(3^n-2^n-1).
%F From _Colin Barker_, Jun 26 2012: (Start)
%F a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3).
%F G.f.: x^2*(2-3*x)/((1-x)*(1-2*x)*(1-3*x)). (End)
%F a(n) = floor((3^n-2^n)/2). - _Wesley Ivan Hurt_, Mar 16 2015
%p A053152:=n->floor((3^n-2^n)/2): seq(A053152(n), n=1..30); # _Wesley Ivan Hurt_, Mar 19 2015
%t CoefficientList[Series[x (2 - 3 x) / ((1 - x) (1 - 2 x) (1 - 3 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 17 2015 *)
%t LinearRecurrence[{6,-11,6}, {0,2,9}, 50] (* _G. C. Greubel_, Oct 06 2017 *)
%o (Sage) [(3^n - 1)/2-2^(n-1) for n in range(1,27)] # _Zerinvary Lajos_, Jun 05 2009
%o (Magma) [Floor((3^n-2^n)/2): n in [1..30]]; // _Vincenzo Librandi_, Mar 17 2015
%o (PARI) for(n=1,50, print1((1/2)*(3^n -2^n -1), ", ")) \\ _G. C. Greubel_, Oct 06 2017
%Y Cf. A036239, A064686 (first differences).
%K easy,nonn
%O 1,2
%A _Vladeta Jovovic_, Goran Kilibarda, Feb 28 2000
%E More terms from _James A. Sellers_, Mar 01 2000
%E a(27)-a(28) from _Vincenzo Librandi_, Mar 17 2015
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