A051180 Number of 3-element intersecting families of an n-element set.
0, 0, 0, 13, 222, 2585, 25830, 238833, 2111382, 18142585, 152937510, 1271964353, 10476007542, 85662034185, 696700867590, 5643519669073, 45575393343702, 367206720319385, 2953481502692070, 23723872215168993, 190372457332919862
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, in Russian, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
- V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, English translation, in Discrete Mathematics and Applications, 9, (1999), no. 6.
- Index entries for linear recurrences with constant coefficients, signature (29,-343,2135,-7504,14756,-14832,5760).
Programs
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Maple
seq(1/3!*(8^n-3*6^n+3*5^n-4*4^n+3*3^n+2*2^n-2),n=0..40);
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Mathematica
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 *) -
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
Formula
a(n) = (1/3!)*(8^n - 3*6^n + 3*5^n - 4*4^n + 3*3^n + 2*2^n - 2).
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
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
Extensions
More terms from Sascha Kurz, Mar 25 2002