A053157 Number of 3-element intersecting families (with not necessarily distinct sets) whose union is an n-element set.

1, 5, 32, 235, 1816, 14055, 107052, 800315, 5886416, 42739855, 307295572, 2193374595, 15571898616, 110121224855, 776543100092, 5464689616075, 38398915520416, 269529406433055, 1890416947176612, 13251578251332755

Offset: 1

Author

Vladeta Jovovic, Goran Kilibarda, Feb 28 2000

Keywords

• easy
• nonn

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 = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (22,-190,820,-1849,2038,-840).

Crossrefs

Cf. A051180.

Programs

Magma

[(7^n -3*5^n +3*4^n +2*3^n -3*2^n +2)/6: n in [1..50]]; // G. C. Greubel, Oct 07 2017

Mathematica

Table[(7^n -3*5^n +3*4^n +2*3^n -3*2^n +2)/6, {n,1,50}] (* G. C. Greubel, Oct 07 2017 *)

PARI

for(n=1,50, print1((7^n -3*5^n +3*4^n +2*3^n -3*2^n +2)/6, ", ")) \\ G. C. Greubel, Oct 07 2017

Formula

a(n) = (7^n -3*5^n +3*4^n +2*3^n -3*2^n +2)/6.

G.f.: -x*(280*x^5-475*x^4+339*x^3-112*x^2+17*x-1)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(7*x-1)). - Colin Barker, Jul 29 2012