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

0,4

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).

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

Cf. A036239, A051181-A051185.

Sequence in context: A015253 A051621 A173427 * A143832 A140841 A062127

Adjacent sequences: A051177 A051178 A051179 * A051181 A051182 A051183

Keyword

nonn,easy

Author

Vladeta Jovovic, Goran Kilibarda

Extensions

More terms from Sascha Kurz, Mar 25 2002

Status

approved