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A051180
Number of 3-element intersecting families of an n-element set.
19
0, 0, 0, 13, 222, 2585, 25830, 238833, 2111382, 18142585, 152937510, 1271964353, 10476007542, 85662034185, 696700867590, 5643519669073, 45575393343702, 367206720319385, 2953481502692070, 23723872215168993, 190372457332919862
OFFSET
0,4
LINKS
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).
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
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);
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladeta Jovovic, Goran Kilibarda
EXTENSIONS
More terms from Sascha Kurz, Mar 25 2002
STATUS
approved