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Number of 5-element families of an n-element set such that every 4 members of the family have a nonempty intersection.
1

%I #15 Sep 08 2022 08:44:59

%S 0,0,0,0,224,21281,1144027,49310674,1915317642,70460566827,

%T 2513684751809,88008877380908,3043421159408080,104321464544910613,

%U 3552122530256316471,120307381384305672102

%N Number of 5-element families of an n-element set such that every 4 members of the family have a nonempty intersection.

%D V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).

%H G. C. Greubel, <a href="/A051367/b051367.txt">Table of n, a(n) for n = 0..660</a>

%F a(n) = (1/5!)*(32^n - 5*30^n + 10*29^n - 10*28^n + 5*27^n - 26^n - 10*16^n + 10*15^n + 35*8^n - 35*7^n - 50*4^n + 50*3^n + 24*2^n - 24).

%t Table[(1/5!)*(32^n - 5*30^n + 10*29^n - 10*28^n + 5*27^n - 26^n - 10*16^n + 10*15^n + 35*8^n - 35*7^n - 50*4^n + 50*3^n + 24*2^n - 24), {n, 0, 50}] (* _G. C. Greubel_, Oct 08 2017 *)

%o (PARI) for(n=0,50, print1((1/5!)*(32^n - 5*30^n + 10*29^n - 10*28^n + 5*27^n - 26^n - 10*16^n + 10*15^n + 35*8^n - 35*7^n - 50*4^n + 50*3^n + 24*2^n - 24), ", ")) \\ _G. C. Greubel_, Oct 08 2017

%o (Magma) [(32^n - 5*30^n + 10*29^n - 10*28^n + 5*27^n - 26^n - 10*16^n + 10*15^n + 35*8^n - 35*7^n - 50*4^n + 50*3^n + 24*2^n - 24)/120: n in [0..50]]; // _G. C. Greubel_, Oct 08 2017

%Y Cf. A036239, A051180, A051181, A051182, A051183, A051184, A051185.

%K nonn

%O 0,5

%A _Vladeta Jovovic_, Goran Kilibarda