A053153 Number of 3-element intersecting families whose union is an n-element set.

0, 0, 13, 170, 1605, 13390, 104993, 794010, 5867245, 42681830, 307120473, 2192847250, 15570312485, 110116458270, 776528783953, 5464646634890, 38398786511325, 269529019274710, 1890415785439433, 13251574765596930

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 -4*3^n +3*2^n +2)/6: n in [1..25]]; // G. C. Greubel, Oct 07 2017

Mathematica

LinearRecurrence[{22,-190,820,-1849,2038,-840},{0,0,13,170,1605,13390}, 20] (* Harvey P. Dale, Aug 16 2015 *)

PARI

for(n=1,25, print1((7^n -3*5^n +3*4^n -4*3^n +3*2^n +2)/6, ", ")) \\ G. C. Greubel, Oct 07 2017

Formula

a(n) = 1/3!*(7^n -3*5^n +3*4^n -4*3^n +3*2^n +2).

G.f. -x^3*(280*x^3 -335*x^2 +116*x -13)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(7*x-1)). - Colin Barker, Jul 29 2012

Extensions

More terms from James Sellers, Mar 01 2000