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

1,3

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) = 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

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A051180.

Sequence in context: A176023 A067220 A057684 * A167254 A140455 A041314

Adjacent sequences: A053150 A053151 A053152 * A053154 A053155 A053156

Keyword

easy,nonn

Author

Vladeta Jovovic, Goran Kilibarda, Feb 28 2000

Extensions

More terms from James A. Sellers, Mar 01 2000

Status

approved