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Number of 4-element intersecting families of an n-element set.
11

%I #20 Jul 04 2019 13:53:07

%S 0,0,0,4,365,11770,278455,5715094,108498285,1963243930,34404675635,

%T 589459538734,9933916068505,165358097339890,2726894329246815,

%U 44648990949187174,727080119853611525,11790570902483264650,190587735542474633995,3073193346666282232414

%N Number of 4-element intersecting families of an n-element set.

%H G. C. Greubel, <a href="/A051181/b051181.txt">Table of n, a(n) for n = 0..825</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>, 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), Discrete Mathematics and Applications, 9, (1999), no. 6.

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (83, -3052, 65670, -919413, 8804499, -58966886, 277278100, -904270136, 1982352768, -2749917312, 2142305280, -696729600).

%F a(n) = (1/4!)*(16^n - 6*12^n + 12*10^n - 9^n - 22*8^n + 15*7^n + 12*6^n - 17*5^n + 17*4^n - 11*3^n - 6*2^n + 6).

%F G.f.: -x^3*(64667520*x^8 - 81966960*x^7 + 42070268*x^6 - 11421992*x^5 + 1766529*x^4 - 152845*x^3 + 6317*x^2 - 33*x - 4)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)*(9*x-1)*(10*x-1)*(12*x-1)*(16*x-1)). - _Colin Barker_, Jul 30 2012

%t Table[1/4! (16^n - 6*12^n + 12*10^n - 9^n - 22*8^n + 15*7^n + 12*6^n - 17*5^n + 17*4^n - 11*3^n - 6*2^n + 6), {n, 0, 50}] (* _G. C. Greubel_, Oct 06 2017 *)

%t LinearRecurrence[{83,-3052,65670,-919413,8804499,-58966886,277278100,-904270136,1982352768,-2749917312,2142305280,-696729600},{0,0,0,4,365,11770,278455,5715094,108498285,1963243930,34404675635,589459538734},20] (* _Harvey P. Dale_, Jul 04 2019 *)

%o (PARI) for(n=0,25, print1((1/4!)*(16^n-6*12^n+12*10^n-9^n-22*8^n+15*7^n +12*6^n-17*5^n+17*4^n-11*3^n-6*2^n+6), ", ")) \\ _G. C. Greubel_, Oct 06 2017

%Y Cf. A036239, A051180-A051185.

%K nonn,easy

%O 0,4

%A _Vladeta Jovovic_, Goran Kilibarda

%E More terms from _Harvey P. Dale_, Jul 04 2019