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

1,2

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).

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A051180.

Sequence in context: A146965 A243693 A364747 * A102231 A365181 A367281

Adjacent sequences: A053154 A053155 A053156 * A053158 A053159 A053160

Keyword

easy,nonn

Author

Vladeta Jovovic, Goran Kilibarda, Feb 28 2000

Status

approved