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%I #17 Sep 08 2022 08:45:00
%S 0,0,13,170,1605,13390,104993,794010,5867245,42681830,307120473,
%T 2192847250,15570312485,110116458270,776528783953,5464646634890,
%U 38398786511325,269529019274710,1890415785439433,13251574765596930
%N Number of 3-element intersecting families whose union is an n-element set.
%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="/A053153/b053153.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (22,-190,820,-1849,2038,-840).
%F a(n) = 1/3!*(7^n -3*5^n +3*4^n -4*3^n +3*2^n +2).
%F G.f. -x^3*(280*x^3 -335*x^2 +116*x -13)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(7*x-1)). - _Colin Barker_, Jul 29 2012
%t LinearRecurrence[{22,-190,820,-1849,2038,-840},{0,0,13,170,1605,13390}, 20] (* _Harvey P. Dale_, Aug 16 2015 *)
%o (PARI) for(n=1,25, print1((7^n -3*5^n +3*4^n -4*3^n +3*2^n +2)/6, ", ")) \\ _G. C. Greubel_, Oct 07 2017
%o (Magma) [(7^n -3*5^n +3*4^n -4*3^n +3*2^n +2)/6: n in [1..25]]; // _G. C. Greubel_, Oct 07 2017
%Y Cf. A051180.
%K easy,nonn
%O 1,3
%A _Vladeta Jovovic_, Goran Kilibarda, Feb 28 2000
%E More terms from _James A. Sellers_, Mar 01 2000
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