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%I #23 Oct 06 2017 21:36:48
%S 0,0,0,13,222,2585,25830,238833,2111382,18142585,152937510,1271964353,
%T 10476007542,85662034185,696700867590,5643519669073,45575393343702,
%U 367206720319385,2953481502692070,23723872215168993,190372457332919862
%N Number of 3-element intersecting families of an n-element set.
%H G. C. Greubel, <a href="/A051180/b051180.txt">Table of n, a(n) for n = 0..1000</a>
%H 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 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, in Discrete Mathematics and Applications, 9, (1999), no. 6.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (29,-343,2135,-7504,14756,-14832,5760).
%F a(n) = (1/3!)*(8^n - 3*6^n + 3*5^n - 4*4^n + 3*3^n + 2*2^n - 2).
%F G.f. x^3*(744*x^3 - 606*x^2 + 155*x - 13)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)). - _Colin Barker_, Jul 29 2012
%F a(0)=0, a(1)=0, a(2)=0, a(3)=13, a(4)=222, a(5)=2585, a(6)=25830, a(n) = 29*a(n-1) - 343*a(n-2) + 2135*a(n-3) - 7504*a(n-4) + 14756*a(n-5) - 14832*a(n-6) + 5760*a(n-7). - _Harvey P. Dale_, Jul 07 2013
%p seq(1/3!*(8^n-3*6^n+3*5^n-4*4^n+3*3^n+2*2^n-2),n=0..40);
%t Table[1/3!(8^n-3*6^n+3*5^n-4*4^n+3*3^n+2*2^n-2),{n,0,30}] (* or *) LinearRecurrence[{29,-343,2135,-7504,14756,-14832,5760},{0,0,0,13,222,2585,25830},30] (* _Harvey P. Dale_, Jul 07 2013 *)
%o (PARI) for(n=0,25, print1((1/3!)*(8^n-3*6^n+3*5^n-4*4^n+3*3^n+2*2^n-2), ", ")) \\ _G. C. Greubel_, Oct 06 2017
%Y Cf. A036239, A051181-A051185.
%K nonn,easy
%O 0,4
%A _Vladeta Jovovic_, Goran Kilibarda
%E More terms from _Sascha Kurz_, Mar 25 2002
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