A051365 Number of 4-element families of an n-element set such that every 3 members of the family have a nonempty intersection.

0, 0, 0, 3, 275, 8475, 192385, 3831093, 71466675, 1285857975, 22632300245, 392522268633, 6734698919575, 114576024346875, 1935649374363705, 32505459713369373, 543014736097852475, 9029329231317194175, 149522990698790644765, 2466942184607949641313

Offset: 0

Author

Vladeta Jovovic, Goran Kilibarda

Keywords

• nonn
• easy

References

• 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).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..825

Crossrefs

Cf. A036239, A051180, A051181, A051182, A051183, A051184, A051185.

Programs

Magma

[(16^n - 4*14^n + 6*13^n - 4*12^n + 11^n - 6*8^n + 6*7^n + 11*4^n - 11*3^n - 6*2^n + 6)/24: n in [0..50]]; // G. C. Greubel, Oct 08 2017

Mathematica

Table[1/4! (16^n - 4*14^n + 6*13^n - 4*12^n + 11^n - 6*8^n + 6*7^n + 11*4^n - 11*3^n - 6*2^n + 6), {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)

PARI

for(n=0,50, print1((16^n - 4*14^n + 6*13^n - 4*12^n + 11^n - 6*8^n + 6*7^n + 11*4^n - 11*3^n - 6*2^n + 6)/24, ", ")) \\ G. C. Greubel, Oct 08 2017

Formula

a(n) = (1/4!)*(16^n - 4*14^n + 6*13^n - 4*12^n + 11^n - 6*8^n + 6*7^n + 11*4^n - 11*3^n - 6*2^n + 6).

G.f.: -x^3*(47062848*x^7 -42816008*x^6 [phone]*x^5 -2170583*x^4 +168932*x^3 -5672*x^2 +2*x +3) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(7*x -1)*(8*x -1)*(11*x -1)*(12*x -1)*(13*x -1)*(14*x -1)*(16*x -1)). - Colin Barker, Jul 12 2013

Extensions

More terms from Colin Barker, Jul 12 2013